I've been enjoying the Spotlight lock screen on Windows 10 and I had thought that a Windows update in November 2020 had caused Spotlight to stop updating its pictures as well as the Like what you see? feature to disappear from the lock screen.
I also tried all suggested solutions of the OP but unlike the OP what did work was trying Spotlight on the lock screen of a pre-existing but rarely used local account where it happened to be working perfectly from when I first logged in.
Based on Reset Windows Spotlight I originally thought that this was due to registry settings in HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows\CurrentVersion\Lock Screen and suggested a solution based on replacing this registry path.
However, after further testing I have discovered that it was in fact changing the Windows Region from United Kingdom to another European country which stopped Spotlight from working. After some brief research there appear to be certain regions where Spotlight is not supported such as Ukraine as documented here.
So if you've recently changed the Windows Region and Spotlight stopped working then the following may fix the problem:
- Disable Spotlight in Settings > Personalization > Lock screen, by setting Background to Picture or Slideshow.
- Performing steps 4 through 6 of How to Reset and Re-register Windows Spotlight in Windows 10 to reset the Lock Screen settings and delete downloaded assets (the OP also documents the manual method of doing this).
- Change Settings > Region > Country or region, to the value which was originally working with Spotlight, which for me was United Kingdom.
- Re-enable Spotlight in Settings > Personalization > Lock screen by setting Background to Windows spotlight.
- Wait a while (for me about 10 minutes) after which Spotlight will update the lock screen, which I actually saw happen in the Settings > Personalization > Lock screen window, but you can obviously also check the lock screen itself by locking the screen using the Win + L keyboard shortcut.
- If you're impatient, restarting Windows might avoid this wait wait I expect.
I did also experiment with using Control Panel > Region > Administrative > Copy settings to set the Welcome screen and system accounts Location to match my Current user location (after setting that using Settings > Region > Country or region to my preferred non-United Kingdom region) but after a while Spotlight again stopped working with this preferred region.