I'm kind of out of ideas then... I don't have any clue why Dropbox would not have that info on your machine but would on mine. I'd say try reinstalling it but I know that's a huge chore. Perhaps some of the AppleScript experts can chime with a workaround.
I'm stumped also. The missing info is clearly available on the Intel processor based iMac. I just check (again), but not on the M1 MacBook Pro. I filed a report with Dropbox, but who knows how long that will take to resolve, if ever.
AppleScript Experts: HELP. Need a workaround!
The only thing I can think of is that the MBP M1 Pro I have is fairly new. It may be that your M1 is older.
It's possible, but mine is also an Air so it has a different chip than yours. That could be an issue too.
Problem Solved!!!
I have a management contact at Dropbox. I explained the problem to him in detail. He found the right party. They suspected that the problem had to do with the fact that I had signed up for "early releases". I turned off that option, uninstalled Dropbox, then reinstalled it. This time, because I had turned off "early releases", it didn't give me an experimental release for the M1. I ran my tests, and it all works now.
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Aha! I suspected it was with Dropbox but of course had absolutely no way of proving that. 
Glad you figured it out and got it working again!