Applying to a job after just accepting an offer
This is an excellent way to burn bridges at two institutions, do not do it.  The interview process for a TT position is long and daunting for everyone involved.  It is also expensive - even if this was a purely virtual interview cycle.  The sheer number of hours that the hiring committee put in to your application and interview when they could have been doing something else in their busy schedule means that they have a good reason to expect that someone who has accepted the job offer they gave will actually do that job.
If you were offered but did not accept, or were still in the interview round, this would be a very different question.  But since you have accepted the job offer then reneging on what you agreed to will look pretty bad on you.
I can see this going poorly for you in several ways:

You apply to the second position, get it, and then try to negotiate a double-job.  Both institutions would reasonably be confused and upset here, with the second job offer probably being pulled and the first institution probably eying you with suspicion.

You tell the first place what you're doing, and apply anyway.  I expect they will be quite concerned that your intention is to jump ship whenever a slightly more interesting position becomes available.

You tell both places what you're doing right from the outset.  The second institution is unlikely to consider you unless you are amazing at what you do - they want a tenured prof eventually, that's a lifetime committment - and still the first place eyes you suspiciously.


The only way I see this working, and it is not ideal, is for you to apply to the second position, get it, and then leave the first to work at the second.  But, you've just gotten a TT position that you seem to be interested in...why would you do that?