No, of course not.
Not that anyone cares about the Constitutional structure of the government any more - BUT - State Legislatures are the sole and final authority over appointment of Electors. This is for a reason - to keep the government in power out of the process.
The Legislatures of Arizona, Wisconsin, Michigan, Pennsylvania and Georgia were perfectly free to meet and appoint electors, or, alternatively, to meet, debate, and file objections with the President of the Senate - and of all six Legislatures, all with Republican majorities - not one did so.
That’s the way I see it as well.
Yes ... Joe Biden was “legitimately” elected in the sense that the electors presented by the State Legislatures did, in fact, elect him. Some of those legislatures appear to have been derelict in their duties.
So the 22nd Amendment is a non-starter regarding Donald Trump’s eligibility for election in 2024.
BUT...
That doesn’t mean that the popular elections held on 03NOV2020 were honest or free of fraud in all 50 States. In fact, we know they were marred by serious corruption in several States. The corrupted popular elections led to State Legislatures choosing electors in defiance the actual will of the citizens of those States.