The hotfix didn't actually include anything to address this specifically, though it did help a couple people. The problem may have been with the patch not installing properly, or some system conflict, etc.
If anyone else has this issue:
A couple of people have provided saves (one just the most recent working save), but the problem was not reproducible.
Rather than just the saves, for anyone else experiencing this, please email email@example.com, with the report.zip file generated by the D:OS 2 Analysis Tool below (or a Dropbox or Google drive link, etc).
Extract the zip file somewhere handy (like the Desktop) and in the AnalysisTool_DOS2 folder, run corresponding executable. It should detect the game install path, but if not you can browse to the 'Divinity Original Sin 2' folder. Optionally run the tests first, and then generate a report (it will be saved in the same location as the Analysis Tool).https://divinity.game/AnalysisTool_DOS2.zip
The report will contain system and game information, as well as your saved games. To reduce the file size you can delete most of the saves from the zip (double click the zip file to open it in Windows Explorer, then browse down to the ..\Savegames\Story folder), just leaving your most recent working save, oldest that will not save after loading and maybe the most recent.
If anyone is providing a link for the report.zip, and doesn't mind a large upload, a full set of saves might be useful, as well.
To check if there are issues not caught by verifying local files, there is a way to effectively reinstall Steam games without having to redownload it.
Right click on the game in the Steam library and select 'Backup Game Files...'. When that is done, right click again and 'Delete Local Content...', then in Windows Explorer, make sure the install folder has either been removed or is empty (before deleting, right click, select Properties, switch to the Local Files tab and select 'Browse Local Files...'), then restore the game backup.
If applicable, disable Steam cloud support either globally (in the client click on the Steam menu and select Settings, and then Cloud) or just for this game (in the library right click Divinity: Original Sin 2 and select Properties, then switch to the Updates tab and check the Steam Cloud section).
Alternately, exit out of the Steam client, or Galaxy for GOG, and just start the game directly from the '..\Divinity Original Sin 2\bin\EoCApp.exe' executable when required.
Next, try browsing to the '..\Documents\Larian Studios' folder and rename the 'Divinity Original Sin 2' subfolder.
This folder contains the saved games, configuration files and a level cache folder. Deleting or renaming it will get the game to recreate it on startup; playing the game from a different Windows user account would effectively do the same thing. With Steam / Galaxy running and cloud support enabled, the client would just download the cloud copy of your existing profile.
After that, start D:OS 2, create a new profile and exit. Copy your latest save from the renamed folder into the newly created profile's ..\Savegames\Story folder. If that lets you load the saves and re-save, move the rest of the saves over (then please zip the renamed folder and email it to support).
If that doesn't help, delete the new My Documents D:OS 2 folder and rename the original back again.