Why won't animated GIFs stay animated after I save them to photos?

Do you have iCloud Photos enabled? Then animated gifs may need downloading from iCloud, before they will play.

You may want to check, if the file you saved to Photos is really the animated gif or just the thumbnail of the animated gif.

Export one of your saved gifs from Photos with "File > export > Export unmodified original". When you view this file in the Finder in gallery view, it should be animated and have the filename extension "gif". If the exported original is not a GIF, you need to view the GIF in your web browser in a separate window, so you can save the linked file to Photos and not just the still thumbnail.

Photos 6 on Big Sur is showing animated GIFs as animated in any album and in All Photos, when you view them enlarged, but not in slideshows.

As a test launch Photos with the Option key held down and create a new, test library.  Import some photos and test to see if the same problem persists. Does it? This tells us if the problem is limited to your current library or is more wide spread.

Next, log into another vanilla admin user account, Set up users, guests, and groups on Mac,  and see if the problem persists. This tells us if the problem is limited to your user account or is system wide.