This sounds like the same problem as T422396 ?

A couple times in the past few weeks the backend seems to have gotten stuck, the number of minutes of lag reported on the UI grows monotonically, and 502s happen if you submit a job anyway and wait around long enough to see what happens. en:User:GreenC thinks this may be caused "when the Internet Archive Availability API goes down and the bot can't search for new archive URLs then gets backed up or something". Perhaps handling this case better would stabilize the bot and stop the 502s.

Per T199660, I assume this should be fixed by changing https://en.wikipedia.org/wiki/MediaWiki:Gadget-charinsert-core.js or local equivalent?

FYI, this is a common problem for me, as https://en.wikipedia.org/wiki/Wikipedia:Closure_requests uses paragraph-initial colorization to indicate how old the various pending requests are.

I think the editors of English Wikipedia can solve this problem on our own by migrating to a new set of templates that are mobile-friendly.

Disabling these two settings stops showing the character-inserting widgets in the UI for me (on English Wikipedia):

Right; images and graphs and stuff generally aren't needed in captions. But sometimes it is necessary to put complicated math expressions in captions to explain what is being visualized.

Yes, you need to click on the image to see the bug, which takes you to e.g.: https://en.m.wikipedia.org/wiki/User:Beland/math_bug#/media/File%3AWikipedia-logo-v2.svg (notice the broken square root in the description at the bottom of the page).

I can now remove these pages successfully.