The Texas suit alleges that significant changes were made to the election rules in the various defendant states, and that these were not approved by the legislatures of those states, but were made by administrative or court decisions. It also claims that differences in local practice and polices made absentee or mail-in voting easier, or invalid votes less likely to be detected, in some counties than in others, meaning that voters in some parts of those states were treated differently than voters in other parts.
Note that this theory has not yet been accepted, or in any way passed on, by SCOTUS. But even assuming that the theory were to be accepted, it would require, at most, strict adherence to the election statutes of each state, and that changes or variances be approved by the state legislature. It would have nothing to say about the actual content of the various state laws, unless those laws treated different parts of a state differently, in which case there would be an equal protection violation.
The Electors clause, cited in this suit, gives to the legislature of each state the power to "direct" how electors are to be appointed. This is done through laws, statutes. The suit cites this clause as a source of authority, and nothing in it could be taken as suggesting a requirement of national uniformity in election law.
I have not yet seen the response to this suit, if indeed one has been filed. It may be that a response would argue that the changes were, in fact, authorized by provisions of the various state laws granting authority to officials. No one knows how the Court will respond to this suit. But even if it were to rule for the plaintiff Texas, that would not impose a national standard, nor permit one state to challenge the provisions of the law of another. It might permit one state to challenge how well another state had applied its own law.