Do the keywords appear in the Quick Group, if you type a keyboard shortcut into the column "Shortcut", when you are in the "Edit Keywords" view? You may want to use this work around, if the problem persists and you still cannot drag and drop keywords.
Just to be sure, have you tried to restart Photos or the system? and have you already tried to toggle the disclosure triangle to the left of "keywords" to reveal or hid the keywords?
I can still drag and drop keywords, but I am using a different system version (macOS 14 Sonoma).
You may also want to check the list of keywords, if one of them contains illegal characters.
As another test, you may want to create a different Photos Library for testing. The keywords are specific for each library. By testing with a new, different library you can see, if the problem ist with your keywords is limited to your current Photos Library or a problem with Photos in your user account or even system wide. If the keywords appear in another Photos Library, something is broken in your current library. Then check the keywords on the new photos you added right before the problem first occurred.