>as the suit alleges, the legislative and not the executive has sole power in making the rules.
And (I'm not a lawyer and I don't live in any of the states in question, so I suppose ymmv) just as Congress passes laws that prescribe standards and practices, but often leaves specific implementation details to the Executive Branch, the same is true in most states.
For example, I don't believe that state legislatures mandates specific voting processes or procedures (e.g., scanners of a specific model from a specific manufacturer, the location of polling places, electioneering restrictions, design/layout of ballots, etc.) and leaves those implementation details up to the Secretary of State and/or state election boards/officials.
In fact, each county (all 3,143 of them) run their own individual elections.
And when there are controversies over either the law or the implementation details, the state courts are the venue to review and resolve those controversies.
That's true in pretty much every state, AFAIK.
The idea that state courts will interpret the law as written by the legislature (in terms of constitutionality, both state and federal, as well as whether the state's executive branch is administering those laws appropriately, etc.) is pretty standard in both state and federal courts ever since Marbury v. Madison[0].
In situations where the court has re-interpreted statutes (and those statutes are how every state has codified its election procedures, whether they be local, state or federal elections), the remedy for the legislature is to modify the law so that it comports with the state and/or federal constitution or making the law more specific in its verbiage.
As far as other states are concerned, they can't be harmed by the outcome of other states' elections, as they either are internal to the state, or they are represented in the Federal government by those elected in the congressional districts as apportioned after each census, or by two senators.
My understanding of Texas' argument of harm is that by certifying the electors fro Biden/Harris, if the two Georgia Senate seats flip Democratic, then, if there is a tie vote in the Senate, Harris is the deciding vote, and as such, Texas' representation in that body is diminished.
But that doesn't make sense, because regardless of who is Vice President, Texas will always have the same two Senate seats.
Again, IIUC, in order to have standing, one must be able to identify specific harm from the issue in controversy. Since Texas' claim was based on one hypothetical (Both Georgia seats flipping to 'D') on top of another hypothetical (a potential tie vote in the Senate), they cannot show specific, concrete harm.
As such they have no standing to sue.
But there are further problems in several of the claims Texas makes against the various states. That of 'laches'.
The idea is that when voters are given a specific set of rules before an election, they must rely on those to hold for that election.
Texas has made claims that a number of provisions of state law in WI, PA and MI (not sure about GA) are either unconstitutional or invalid.
The problem with a number of those claims is that the laws in question were in place far (one, in WI I believe, since 2016) in advance of the election.
The idea of 'laches' is that if those rules were already in place months to years before the election, the time to challenge them was before the election -- before the voters had to rely on those laws when casting their votes.
Since Texas did not do so (as well as many of the other lawsuits filed), changing the rules ex post-facto would disenfranchise the voters who relied on those rules when the election was held.
This article[1] explains all this and more much more succinctly than I did.
And this article[2] goes into other details of the issues, again explained better than I ever could.
[0] https://en.wikipedia.org/wiki/Marbury_v._Madison
[1] https://electionlawblog.org/?p=119476
[2] https://reason.com/volokh/2020/12/09/how-the-supreme-court-c...
Edit: Fixed link numbering.