We use the semantic <del> and <ins> tags to mark deleted and inserted content. As far as I know this is correct, and the problem here is on the side of screen readers that ignore them.

Here's an article I found about accessibility of those tags: https://adrianroselli.com/2017/12/tweaking-text-level-styles.html. Takeaways:

• We could add messages to be read before or after the marked content, e.g. "deletion start" and "deletion end" etc. However, this would potentially conflict with any screen reader software that actually has built-in support for this.
• According to the article, NVDA with Chrome supports these tags since 2018, and JAWS added support in 2020 but then removed it "in response to customer feedback". Perhaps there is some well-hidden option you could use to enable it?

In my own testing with Windows Narrator, I could set the option "Change the level of detail Narrator provides about text and controls" to "5 — All text details", which made it read out the background color of the text (and useless detail about fonts), but it still did not speak the semantic information about it being deleted or inserted.

Yeah, it is perhaps a screen reader problem. I think in JAWS the option to read inserted/deleted text is only available in Google Docs.

This issue also presents in Safari/VoiceOver btw, so I filed https://bugs.webkit.org/show_bug.cgi?id=226329

Update: JAWS has re-added the reading out of del/ins semantic markup as a togglable feature ... it defaults to being on (I used the Wayback Machine to link to the announcement as this isn't a stable URL). Now that it can be turned on and off, I imagine this feature will stay around for the long term.