Sorry about not replying earlier! Didn't have time until now to puzzle this out. I have an M1 MacBook Pro on Sonoma and a 2013 MBP on Big Sur (OS 11.7.10) and Airdrop is working. Does bluetooth currently work otherwise on both computers? You probably have bluetooth keyboards and/or trackpads or mice, so if they are fine, that's not the problem, of course. Here are some possibilities:
1) Turn bluetooth off for a few seconds, and then back on again. Probably a good idea to hav both computers' bluetooth off at the same time.
2) On both computers, click the apple symbol on the menu bar and go to System Settings/General/Airdrop & Handoff, and make sure that "Allow Handoff between this Mac and your iCloud devices" is turned on. This may have been turned off during the upgrade.
If Handoff is already on, turn it off, wait a minute, and turn it back on.
3) There is always the old standby of restarting your computer - or computers, in your situation.
4) If none of these help, you could try reinstalling Sonoma. It's possible that one of your computers had an issue with the update.
How to reinstall macOS - Apple Support
This all I can come up with, from searching in the Apple Support and Support Community websites. You can try reaching out to Apple Support directly here (scroll down to where it says Get Support):
Official Apple Support
