Has anyone immediately terminated an employee when they reported to their manager that they were looking for another job because they do not want to come back to the office?

No, and I wouldn’t terminate them immediately or maybe never. It’s a good thing they are looking for another job and that they felt comfortable enough to tell their manager.  Continue to hold them accountable until they leave the firm.  I would consider termination if there was a mandate requiring a return to the office, with a deadline to comply, and the employee blatantly refused to return to the office.  This would be insubordination.   However, be cautious and find out why they perhaps NEED to work from home.  Is there a legitimate reason under ADA? Assuming that is not the case in this situation.

Yes. I have seen where this was accepted as a voluntary resignation effective immediately in the U.S.  

Not sure which country we are referring to here. If this is for India, we cannot and should not directly terminate. In such a scenario, it is essential to send an absconding notice with show cause, and if the employee still refuses to respond or confirms in writing that they are not willing to join back, we can proceed with termination.