~Fusion Bolt / Fusion Flare boosted damage~
Smogon: "Power doubles [for Fusion Flare] if the last move used by any Pokemon this turn was Fusion Bolt."
Bulbapedia: "The base power of Fusion Flare will double if any Pokémon has successfully used Fusion Bolt previously in the same turn, with no intervening moves in between, except perhaps for failed moves."
I tested this pretty extensively (87 tests in White, 58 in Scarlet). In essence, if Fusion Bolt and Fusion Flare are used in the same turn, the second one used will be boosted if there are no
successful intervening moves. I don't know quite how it works in PS, but from observation PS seems to keep track of used moves by when they are clicked or maybe when they are listed in the log, whether or not they are successful. For Fusion Bolt/Fusion Flare, the important thing should be if the intervening move(s) actually took effect. For attacking moves, if they successfully deal damage (regardless of other effects). For status moves, if they successfully modify a stat, change the weather, steal a move, swap abilities, etc.
Here's a video of examples from Pokémon White. All are accurate for gen 9 as well.
PS gets these correct:
Paralysis
Asleep
Confusion self-damage
Truant skipped turn
Giga Impact recharge
None of these scenarios have an intervening "Pokémon used move!", and so the boost is present. (It's convenient that Reshiram and Zekrom do the same damage to each other with these moves. In these examples, an unboosted Fusion Bolt or Fusion Flare hit does about 23% damage, and a boosted hit does about 46%.)
PS also gets calling moves correct:
Sleep Talk
Assist
Mirror Move
If these moves call Fusion Flare after Fusion Bolt it will be boosted. They also cannot block the boost on their own if used as an intervening move, but rather it's if the called move succeeds or fails.
Fly 1st turn - Fusion Flare should be boosted but is not
Fly 2nd turn - Fusion Flare is correctly unboosted
Struggle fail - Fusion Flare should be boosted but is not
Struggle hit - Fusion Flare is correctly unboosted
In addition to the above if a move fails by type immunity, target's ability, skill swap ineligibility, healing at full HP, protect, missing on accuracy, trying to set two screens on one side of the field, trying to raise/lower stats beyond +/-6, or being unable to set the weather, then it will not block the Fusion boost. I'm sure I'm forgetting something... In a triple battle, you could fit four different fails between Fusion Flare and Fusion Bolt and the boost would still work which is a little silly haha
There are edge cases of course. Does the success of a move depend on one or all of it's effects happening? Short answer: no.
A damaging move that can alter stats is successful whether or not it alters any stats.
Chilly Reception is successful if it starts to snow whether or not the Pokémon can switch out.
On the other hand, crash damage moves like High Jump Kick have the effect of taking a sort of recoil only if they are not successful. Moves like Mind Blown are guaranteed to take recoil whether or not they are successful in dealing damage.
Just as an aside, these results line up with when a move animation plays or doesn't play in-game. If a move animation plays between Fusion Bolt and Fusion Flare, the boost will not happen. It's like recoil, crash damage, and Mind Blown-style recoil happen as a separate thing from the move and it's animation. Here's an example of
Confuse Ray vs Magic Bounce where the blocked move doesn't animate, but the rebounded move does, and so Fusion Flare is unboosted. The only move animations I can think of that still play but don't inhibit the boost are the invulnerable turns of Fly, Dig, etc.
And lastly, I want to emphasize this only has to do with moves. If a used move activates a target's ability that blocks the move and then does it's own ability-specific effect (Water Absorb, Lightning Rod), the Fusion boost would still be available.