Is the GOP's challenge of the electoral college vote just a publicity stunt?

publicity stunt? Not sure if that is the right phase or not but yes. There is no chance it will be overturned, none at all, so all this is for show, talking points. It has been played up by the media and the fearmonger too, that is also show/stunt, whatever.
Regardless of all this crap though, there are still some fundamental issues that will need to be addressed before the next election.
Does an individual or group have the authority to alter election laws even though federal states, all changes must go through the states legislative process.  Becouse that happened in multiple states. Then we have the ballots being separated from their envelopes so they can't be verified. That wouldn't be such an issue if the software for signature verification hadn't been changed the night prior to the election.  Which is also questionable as to the legality of it.  All three have been publicly documented as to have happened.

When Democrats challenged the electoral college vote in 2001, 2005, and 2017--was that also just publicity stunts?  Or is it only when Republicans do it?

This isn't about Trump... it's about the next decade of elections...

This is a message to the states that abandoned standard validation policies for mail-in ballots that the "emergency" excuse will not fly next time around.  At the state level, election officials will quietly agree and the GOP agitators in DC will drop their demands for greater scrutiny...allowing those with cushy lifetime jobs at the state level to stay in place...