Clearly I have no idea what I have done wrong or what is needed to fix this problem. Every other homebrew install/reinstall/update/upgrade works as expected. It is only sqlite3 that does not.
It looks like your user may not have permission to tho the /opt/homebrew/lib/python3.11/site-packages/__pycache__ folder. You might want to ensure you can read and write to that directory.
be careful, verify the date of the answers you get. A lot of no longer viable stuff is still there and can catch you if you do not check. I used to use it a lot but over time it’s become more and more unreliable with old now incorrect answers getting upvoted just because of age and the moderation is IMO draconian if you try to ask a similar question specifically requesting newer data and tools. Yours gets flagged and everyone points you to the old answer that won’t work due to version changes.
Indeed know that only too well from using ChatGPT to bootstrap some perl, sed, awk code. For example, there was no indication from ChatGPT of what version of sed its generated examples were using; macOS has BSD’s version by default but the generated code expected GNU’s version.