1. Are there any non-assumed STAB options worth discussing?
I don't think they're controversial in the slightest, but Leech Seed and Toxic Threads are ones I find interesting. There has been a lot of discussion on discord about Mortal Spin as well and I'm mixed on that at the moment.
2. Are there any other coverage options that are worth bringing up here? Other Ground / Fire options, or other coverage types?
Mystical Fire is the main coverage option I've been thinking about. This is primarily due to it being potentially weak enough that offensive sets may eschew it. If CAP 38 gets proper Fire / Gound coverage (Flamethrower / Fire Blast) I really don't think it can get almost anything else. STABs + Meteor Beam + Earth Power is already very good. Some type of trapping move (i.e. Infestation or Fire Spin) is also interesting.
3. How should we handle utility here? Are there any utility options that are important to nail down before stats, or can they wait for movesets?
I think it would be good to at least decide on penalties for some of the more popular options before stats. It is a shame Aromatherapy is dexited because that could be an interesting option for defensive sets.
4. Should Meteor Beam be a required move or an optional move? Are there any alternative setup options?
I'm not really sure which Meteor Beam should be. Personally, I'd have it be required, but I also don't know how that impacts later stages. What I really don't want to happen is for Meteor Beam to have a penalty if it is avoidable. If there is a penalty no matter what then fair game. Sure, there are technically alternatives to Meteor Beam, but also not really. Meteor Beam is pretty unique due to somehow being balanced for its power level. It is coverage, but it isn't reliable coverage since it is a one time boost against most teams and CAP 38 potentially 'requiring' it for multiple Pokémon (Yveltal + Ho-Oh teams in Ubers for example). As mentioned above, Electro Shot has implications with weather that many folks, including myself, would rather avoid.
Other stuff / responses
If CAP 38 does indeed get Meteor Beam then I'm genuinely unsure what offensive sets really need beyond what has commonly been discussed. Sure there is a debate about Fire coverage, but that can also be addressed in the stat stage. Ground coverage was more popular and it is more powerful, limiting defensive counterplay. It is the defensive set I'm a little more concerned about as Grass / Poison is checked or walled by quite a few bulkier Pokémon and Toxic isn't the progress making tool it is in Ubers. It is definitely possible that defensive CAP 38 can carve a niche with its current traits as a fast, fat wall that defensively handles several prominent offensive Pokémon.
The defensive set doesn't have to be the best set to be mini Eternatus, but it should be something that is at least considered for a decent amount of teams at some point in the building process. There has been a lot of criticism of many proposed support moves not feeling like Eternatus and that is true, but I'm also not sure how much that matters? I'm also not sure how much people care given it was pretty likely we would end up with this conundrum when choosing the typing and ability. While Eternatus's utility movepool lacks depth, it somehow produces variety within the defensive set and ends up being impactful. If the defensive set needs more tools than what it currently has it will have an 'anti-Eternatus' vibe because we will likely be forced to go off-typing. As with most things, the devil is in the details. Looking at what has been suggested so far...
Lecch Seed | This isn't an assumed move, but fine, underpowered even. It is a nice thing to have even if it isn't a staple of defensive sets.
Knock Off | Is this anti-conept? Sort of, but so are most things mentioned outside of Mortal Spin. It does fit the angle of useful on defensive sets, but not offensive that I like. That being said, it feels a bit shoehorned because of the power of Knock Off. I lean more towards no than yes, but it seems like it should be possible to balance.
Wisp | I'm not a fan of CAP 38 being able to spread burns or paralysis, but am somewhat amenable to burn. I don't like it, but somewhat see the vision I guess?
Thunder Wave | Lord have mercy...please no! CAP 38 can't be statused and I feel that status immunity should come at the cost of being limited to spreading poison or Toxic. Even then, one common way to handle Eternatus is to take away its speed via paralysis to let those midspeed Pokémon beat it down. Turning that dynamic on its head is something I just really really do not like.
Metal Sound | Something in my head says this could lead to some pretty unpleasant gameplay loops, but another voice says it is very easy to take away if it causes issue.
Mortal Spin | I'm neutral on this because I do not have the metagame knowledge to take a concrete stance. Mortal Spin has the vibes of a move that a mini Eternatus could reasonably have access to, but there probably a lot of reasons why it shouldn't. I don't know enough about the entry hazard metagame in CAP to know.
Trick | I both like and am worried about this.
Matcha Gatcha | I'm not the biggest fan for a few reasons. First is that 90% accuracy sucks and is something we will end up cursing Meteor Beam for after release. However, that still gives you the boost and for Matcha Gatcha it really is the only downside. The upside is that Matcha Gatcha does not seem like a move that offensive sets will utilize. I do have concerns about it being a bit toxic on defensive sets as they will both be fat enough and have the longevity to burn fish. Sure it may miss sometimes, but that comes with the burn chance, more pp, and higher BP than Giga Drain. If Matcha Gatcha ends up being worthwhile using on an offensive set then that likely comes at the cost of the defensive set's viability which I don't like.
Encore | This feels weird and I don't know enough to know if it is a good or bad idea.
Salt Cure | This is really cool, but I have a voice in my head that says this is going to be too busted, espcially with Ground-type coverage locked in. There are probably a fair few Pokémon that could muscle through CAP 38 with Tera Poison (or Substitute), but Earth Power exists. One of the nice things about Grass / Poison / Ground is how well it handles common Tera types and I get the feeling Salt Cure would push that over the edge.
Apple Acid | I'm an Appletun fan...but there is an alarm bell ringing in my head about how this could lead to degenerate gameplay loops. Yeah 80 BP isn't anything to write home about, but damn is that effect powerful. Sure it has an 'average power' of whatever over a couple of turns, but this is exacerbated by CAP 38's Speed which will make it substantially more difficult to switch around. Whilst don't know what Speed CAP 38 will end up with, the pool of Pokémon that both outspeed and threaten it will be limited. Maybe Apple Acid would be reasonable on Meteor Beam and defensive sets, but I can easily see it getting out of hand on Life Orb or Choice Specs sets. It also seems like a god damn nightmare to balance when it comes to stats because broken on one set is still broken.
Additional Suggestions
Phasing | I'd be surprised if Eternatus recieved Dragon Tail for any reason beyond it getting nearly every Dragon-type move. While Eternatus can phaze, the main motivator is utility that deviates from the controversy surrounding the entry hazard metagame. CAP 38 wouldn't be the fastest phazer, but it isn't as though Roar Zamazenta is in anyway a threat and it could be useful on defensive sets for Pokémon such as Chuggalong and Ramnarok without having to run Earth Power. I'm sure there are others, but those were the first two to come to mind.
Partial Trapping | I'm saying partial trapping because the concept is more important the specific move. Fire Spin Eternatus is a meme, but I can see the potential for some teams that could make use of CAP 38 removing specific roadblocks. Part of the reason I've gone with the general concept over a specific trapping move is that maybe trapping Mollux to remove it with Earth Power is too strong, but Whirlpool exists. I lack metagame knowledge to get into the specifics. I wanted to mention it here in case it happens to be something that could require a penalty.
Mystical Fire | I've specified Mystical Fire because it is weak enough that offensive sets likely would not entertain it and this would be an alternative to Earth Power on defensive sets that can annoy switchins and prevent them from being setup fodder for something. If offensive sets are using it then I wouldn't want to consider it without some sort of penalty. Additionally, if CAP 38 gets generic Fire coverage I think it should be restricted from nearly every move mentioned in this thread. I voted against Ground coverage because I think it is a little too good, and I have serious concerns about Ground / Fire coverage being balanced via stats without severely impacting the efficacy of defensive sets.
Final Thoughts
For what is it worth, I do think some folks get a little tunnel visioned in attempting to replicate what Eternatus does in Ubers 1:1 and I don't think it is possible to that with the established kit while creating a balanced CAP. That is also fine! We are inspired by Eternatus, not replicating it. Eternatus's flexibility comes from having multiple viable sets, but of varying strength that ebb and flow with metagame developments. Maybe when CAP 38 is released the offensive sets have the spotlight and metagame developments later push the defensive set the forefront. If CAP 38 can do that then I believe it truly will be a mini Eternatus and it currently probably isn't far off that. Giving defensive sets a couple of tools would likely get it there imo.