Sorry, for the delay. I read your question days ago in my RSS-reader and marked it as read but forgot to answer here.
I'm on version 2.4.19 and the bookmark feature has been working perfectly fine but out of the blue (I've not edited any files on the server) I now get given an error page when changing a bookmark's name and leave the tags box blank
Ok, when I look into the relevant code of version 2.4.19 (and also version 188.8.131.52) I see no code that could cause the error messages you show in your screenshot. So we have to assume, that you doesn't run a clean install of any of that versions.
To be clear, the relevant function
getBookmarkTags is actually located in the near of the named lines in the screenshot (functions.inc.php #2842, #2843).
If I change the bookmark's name and leave the tags box blank it goes to this error but If I then go back to my bookmarks the bookmark name has indeed changed.
That is a misbehaviour because one can change the name as well as the tags in one form but both data points should be handled independently (and correct).
If I change the bookmark's name and add tags I do not get the error.
I'll investigate it further (with a comparision to newer versions).