In a nutshell: Yes, state legislatures are responsible for deciding the "Manner" used to appoint Presidential electors. And in most states, the "Manner" set forth by the state legislature is "general ballot at the general election."
And as long as that process occurs, stuff like disputes over deadlines, drop box locations, signature verifications, etc stay squarely in the realm of election administration. As Judge Brett Ludwig (a Trump appointee) put it:
> But issues of mere administration of a general election do not mean there has not been a “general ballot” at a “general election.” Plaintiff’s conflation of these potential nonconformities with Constitutional violations is contrary to the plain meaning of the Electors Clause. If plaintiff’s reading of “Manner” was correct, any disappointed loser in a Presidential election, able to hire a team of clever lawyers, could flag claimed deviations from the election rules and cast doubt on the election results. This would risk turning every Presidential election into a federal court lawsuit over the Electors Clause. (Internal citations omitted.)
(Source: https://www.scribd.com/document/487916351/12-12-20-Trump-v-W...)