Door keeps autolocking

Lunar-Eclipse

Have you tried taking the battery out of your key fob? It might be something as simple as the lock button is stuck on the fob. Or the micro switch beneath it. Take the battery out and try your other fob.

The obnoxious rapid beeping sound you're hearing. Is that the same lock/unlock sound you would normally hear when you press the door request switch but sped up as if you were repeatedly clicking unlock?

If you were not previously hearing the lock/unlock sound have you checked your extended storage switch? That turns off features like the lock/unlock chime.