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Patience seems to be the most common solution to this problem. no rhyme or reason why downloads start or stop, at least in my experience (so I don't even bother checking, only look for when update is available).
Maybe a Tesla Urban Legend but I remember seeing posts that said to remove any USB devices for Tesla Cam and/or music and reboot. Hope that works. Alternative is to create a service appointment from the app, they can check remotely and possibly help. Good luck.
Make sure the car has access to WiFi and has been configured to use it.
I put a WiFi access point in my garage to guarantee the car has good access.
If a USB stick has ever been configured to be "bootable" it must be removed so the car can't try to boot from it.
I have a USB stick in my car and it does not prevent receiving new software.