Just so we're entirely clear about what happened here:
These 8 petititions were all requests to expedite review (of cases that SCOTUS was most likely not going to review anyway). By declining to expedite review, virtually all of the cases became moot as soon as the electoral college votes were certified, and if not then, then certainly after inauguration. And now that they've done this action today to decline to expedite review, they won't act on any of these again until after inauguration anyway.
Two other related cases may still eventually get heard, both from Pennsylvania, however they are about issues that all parties have already acknowledged would not affect enough votes to change the presidential election. This case has already come up to the US Supreme Court once and Justice Alito, who handles emergency petitions from the circuit court that contains Pennsylvania, ordered Pennsylvania to segregate the ballots in question so they could be counted separately if needed, subject to later litigation. Pennsylvania in turn complied and ordered all of its clerks, etc to do so, so the number of ballots that arrived late is known and is (far) less than the margin by which Biden won the state. A bit under 10,000 votes came in that would be in question per these cases, and Pennsyvlania has determined that aside from the presidential race (where 10,000 is clearly not enough to change anything since Biden won by around 80,000) no other federal races were impacted either. So in terms of 2020 itself the case is moot.
If SCOTUS agrees to hear those it would purely be advisory for future elections, and even though courts don't really like hearing cases about things that are no longer relevant, they also really hate election lawsuits under tight timelines. So they might hear a case about these PA issues, just so they can opine about the issues at hand and clarify things for 2022 and beyond. In my opinion, these cases are pretty bad examples for SCOTUS to use to set any case law so I think it is more likely that they pass, but who knows.
The gist of the PA case is:
The Pennsylvania state supreme court, interpreting Pennsylvania state law and the Pennsylvania state constitution, required the state to count absentee ballots that arrived up to three days late as long as they were not clearly postmarked after election day (based on evidence from the post office that delays would occur in such a way that Pennsylvania's statutory deadlines would result in some people who followed all the rules and deadlines that were intended to help them vote by mail end up with their votes not getting counted due to circumstances that were unforeseen when the state's election law was enacted). Article I of the Constitution places the power for setting the "time, place, and manner" of elections in the hands of state legislatures, subject to laws made by the US Congress, which has enacted a law setting a uniform day for these elections, which we know as Election Day - whichever day between November 2 and November 8 is a Tuesday in a given year.
Pennsylvania republicans are challenging that 1) the state Supreme Court had the authority to do anything with respect to the "time, place, and manner" since they say that's a power of the legislature, and/or 2) whether what the result of what the court did (ie allowing the counting of mail in votes that arrive up to 3 days late) violated the federal statute that sets one election day nationwide.
Both arguments have serious issues with them.
The first argument more or less says "because the US constitution says it is the state legislatures responsibility that means it is 100% the state legislature's responsibility and there is no mechanism for a state court reviewing whatever the legislature says". Obviously that's not the case otherwise there wouldn't be lawsuits in state courts related to elections, which there have been long before 2020... The purpose of the Pennsylvania Supreme Court decision was to interpret the constitutionality of the voting system that was going to be used, per the Pennsylvania State Constitution. There is ample case law that says that state election law MUST comply with state constitutions, so there really should be no argument here that a state court could review. All state legislation is subject to state constitutional law. There's no special carveout for elections. Ultimately the Pennsylvania Supreme Court ruled that the unforeseen postal delays impacted the existing voting law so much that they became unconstitutional because of how it would disenfranchise voters whose ballots would fail to arrive on time, even though they would request a mail in ballot on time and maybe would even put them back in the mail on time, through no fault of their own. So in summary, the Article I provision that gives power to state legislatures very clearly does not give it solely to them - it is still subject to review for constitutionality under the state constitution. So it is pretty much guaranteed that SCOTUS would not agree with the main argument and say that the PA supreme court wasn't allowed to review. If we then assume that the PA supreme court was within their rights to review, what SCOTUS could instead say here to overturn on these grounds would be "yes you could review, but you reviewed incorrectly" ...but that is also not a plausible thing for SCOTUS to do here, since the PA Supreme Court said the election law was an as-applied violation of the Pennsylvania State Constitution, not the US constitution, and SCOTUS is highly unlikely to step in and say no actually we're the experts on your constitution and you interpreted it wrong. As a matter of law and policy, SCOTUS does not review state court judgments in cases that only have to do with state law. The only way SCOTUS could review therefore the PA court's decision as pertains to the state constitution is if the state court ruling violated the US constitution, but the plaintiffs haven't articulated clearly how that could be so. If the state court is authorized under the US constitution to review, then surely no decision they reach is inherently unconstitutional. It could be that this particular decision is unconstitutional if it created an unconstitutional system itself, i.e. the PA Supreme Court couldn't decide that everyone named Steve's votes would count double, since that violates one-person one-vote. But it's hard to say what the violation would be here in allowing mail in votes to arrive late, since it was applied equally to all voters statewide. All in all, this argument doesn't seem very likely to succeed to me.
The second argument that the federal statute designating one day as Election Day somehow forbids counting mail in ballots postmarked before but received after election day has its whole own other set of issues. The general interpretation (and there is no real division among courts on this...) is that votes must be cast on or before election day. This is why early voting is a thing, this is why mail in voting is a thing (no one can have a mail in vote that is both cast and received on election day... the mail doesn't work that fast!). No one has ever won a case to my knowledge that the federal law designating one single day as election day means that votes received by mail after, but postmarked before, Election Day cannot be counted when a state has decided that they would like to do so. Indeed, Pennsylvania is not the only state that accepts such ballots. A number of states have allowed this even before 2020, and some more began doing so for this cycle due to the increased amount of mail in votes and expected postal delays related to COVID. Nor is 3 days in any way unusual or "generous". Some states allow votes that arrive even 2 weeks after election day. If Pennsylvania isn't allowed to do this, then neither are like 20 other states. Even beyond the 20 or so states that accept ballots received by mail after election day, there's all kinds of other votes that are accepted after election day, such as cases where an absentee ballot received on or before election day and is "cured" after election day or cases where military/oversees voters might have deadlines that allow them to have their votes counted late, even if other absentee votes are not, etc. There's just no way that SCOTUS takes the bite here and throws general chaos into the world by requiring that ALL votes must be received by election day, when the current state election law patchwork has been working "fine".