Your images are held locally, so they are there for you anyway. Also, check our post that looked at what happens if you stop your subscription:
Oddly, I just had this happen again yesterday - Develop Module, 900 photos to run through, after a couple of dozen LrC just kept flashing through the Filmstrip at the bottom. My disappointment? Brand new machine, different OS (now Monterey), latest version of LrC (11.4.1). And I am absolutely no...
Lightroom will re-compute if you've made adjustments to the image(s), as the Standard Previews will be out-of-date.
Smart Previews work differently - they are used as a proxy file if the main photo isn't there, or in place of the original if you have the box ticked in Preferences to use them...
I just ran through it again this morning...and it worked. I know the steps were the same; yet there must have been something!!
I shall carry on trying to repro then (I tried it several times since your post, can't break it now!!!
This is more likely a permissions issue, there were some recent changes to Monterey. Lightroom is dependent on what the OS presents, there's been no changes in its operation.
Check through this blog (check Full Permissions)
Given the recent events you mention, I suspect it's simply that previews haven't been built, and each time you're moving to the next photo the preview needs building.
To check, select all the photos in the folder you're going to work through, then Library > Previews > Build Standard sized...
You don't specify the version of Classic you're currently on; there have been two updates in 2022. Can you check which you're having the issue on? Then try reverting to the previous version, see if that rectifies? It's hard to comment without knowing actual versions. Then we can come up with...