At this point, I can confirm that Pro and Plus account types with DropBox are not currently supported, and will generate the "Please sign in with a work account" message with the DWG History feature. We hope to correct this issue with upcoming updates (very soon!) for the 2021 AutoCAD products. Sorry for the inconvenience.
For now, there is a workaround, but it's completely unsupported by Autodesk and Dropbox, and could potentially cause synchronization problems with your local DropBox client operation. There's a file called info.json, which our DWG History feature uses to interface with DropBox, and it is located in:
%LOCALAPPDATA%\Dropbox\
which resolves to C:\users\<your username>\appdata\local\Dropbox\
On a Pro or Plus account, the last line of the file shows the subscription_type: as either "Pro" or "Plus". Edit the info.json file to replace "Pro" or "Plus" with "Basic". Save the file, being sure not to add anything extra onto the file extension (such as .txt), relaunch AutoCAD, and then it should work. Just to be on the safe side, make a copy of that file prior to modifying it, in case you need to swap it back out.
When the DropBox client software starts, it checks the account type and resets the info.json file accordingly, so if you've changed it to "Basic," then closing/relaunching Dropbox or restarting the computer will automatically switch it back to your actual account type, so you'd need to modify it again. However, you can prevent that switch back from happening by making the file read-only after you make the modification. In my testing here, closing/relaunching Dropbox doesn't (can't) force the change on the JSON file, and it keeps working with AutoCAD's DWG History feature.
Again, all of this is completely unsupported, but should enable your usage of the DWG History feature with Dropbox Pro and Plus accounts.

Zac Travis