This is nothing like 2000, which was driven by actual uncertainty of the outcome; this is entirely driven by Trump's ego and narcissism.
Hyperbole. Many people aside from Trump are suspicious and have questions about the election results. I am suspicious and have questions about the election results. I have the luxury of being patient and seeing how this all shakes out, because I'm not the one who ran for President.
The people who are suspicious and have questions about the election results are either coddling Trump (to avoid getting fired, attacked, or losing votes in their next election) or are part of the grift, either as perpetrators, unwitting collaborators or marks. Bill Barr says no evidence of sufficient fraud to change anything; Chris Krebs got fired for saying as much. Numerous Republicans stand by the integrity of the election they ran in their state. Many Congressional Republicans privately want Trump to give it up, but won't say so in public.
In 2000, Republicans knew that the Florida result could be overturned easily in a recount; that's why paid Republican operatives including congressional staffers stopped one county recount in the "Brooks Brothers riot" (
https://en.wikipedia.org/wiki/Brooks_Brothers_riot ). The only people trying to stop vote counting this time were Trumpies, and nobody who prefers Biden's victory has done anything to stop the recounts because they have absolutely no fear they can overturn enough states to change the outcome. The threats that result are damaging, though, as Gabriel Sterling, a Republican election official in Georgia, states "I can't begin to explain the level of anger I have right now over this".
https://www.youtube.com/watch?v=JzBujmlI3zIThere's an older and more authoritative definition, though. It's not formally defined in the Constitution, but it's strongly implied. And unlike the GSA admin's assessment, it's based on reality not a projection. It's when the Electoral Collage votes, and picks a president. (Or the same happens via one of the contingent methods, as described in the Constitution.) That's the final, conclusive determination of the President-elect.
The explicit definition in federal law is clearly stronger than your made-up implied definition. And it's the only one with any actual consequence other than the PR you're desperately trying to spin. But I applaud your endorsement of penumbral rights found in the Constitution. Note that Congress can still contest the Electoral College votes in early January, so the Electoral College vote is not really final anyway.
A third definition is when states with 270 electoral votes certify their results. Which isn't final, because states choose their electors, and electors can do what they want.
They've been certified in all the states Trump contests, and President-elect for more than a century has been used before certification or electoral college vote. Note that electors are not free to do what they want in every state; the Supreme Court upheld state laws forcing an elector to vote as committed by the vote and their election laws. The move to get Trump electors to vote against him in 2016 was obviously doomed - electors are longtime party operatives, chosen for their loyalty - but it did set a marker when two voted against him (and another resigned and was replaced because he wouldn't vote for Trump or be faithless). Biden is mainstream enough that it's not going to happen this time at all.
The fourth definition is when one of the major candidates concedes.
Trump tweeted that Biden won back on November 15th. He loaded it with a lot of self-serving excuses about fraud, voting machines and the media. But a concession would make someone President-conceded-to; concession has never determined who was elected.
The fifth and weakest definition is based on various third party projections (like the AP's) shortly after the election results come in.
They took until November 7th this time. Republicans had deliberately arranged for delayed counting of mail-in ballots in Pennsylvania, Michigan and Wisconsin. Everyone was leery of making predictions that turned out badly, given that exit polling was useless and there was no experience with so many mail-in ballots. Fox News' early call of Arizona looked like it might have been a mistake, and most other outlets declined to call that one until well after Pennsylvania settled it. The "red mirage" that led Trump to claim multiple states was obviously wrong by the day after the election, though.
But the projections are for Biden, the cases disputing the results are winding down, states have begun to certify their results, and the GSA admin's letter has started the transition process in his favor. He's almost certainly going to become the President-elect, so terms like "presumed President-elect" or "presumptive President-elect" are appropriate. But stating that he is the President-elect, full stop, with no qualifications, is simply incorrect.
I understand that you're disappointed with the result, but Biden
is President-elect; "Pat doesn't think so" is not going to get onto any list of President-elect definitions. Not sure who would have standing to sue to stop them using the title on Biden's presidential transition web site,
https://buildbackbetter.gov/ , but maybe you should give it a try if Trump won't.
It's an easy mistake, given the weight of tradition, so it's no surprise people were initially confused, and it took a while to work out the details. But at this point, the news media have had plenty of time to look it over, correct themselves, and put a qualifier in front President-elect. Since they've chosen not to, that means they're deliberately lying.
Kool-aid overdose (sour grape flavor). They've looked it over and stuck with it because it's true. Media mostly prefer the fifth definition you list, because it flatters them with the most importance. But I encourage you or Trump to sue Fox News over this. Be aware that they've defended lawsuits by claiming they're entertainment rather than news, and Sean Hannity recently admitted that he doesn't vet the information on his show.
Note that many media are also referring to Biden as the 46th President; that's one thing Trump
could prevent, by resigning and making Biden 47th (or beyond). Add that demand to your lawsuit, please, for the entertainment value.