Let's change the way you're looking at this - you keep thinking it's something wrong with the way your forum is set up, but what if the issue is that your forum is being overrun by spam bots creating too many connections because too many spambots are visiting the site at the same time (along with search bots, AI scrapers, and whatever else is also visiting).
- Have you looked at your server access logs for the periods in which the error occurred?
- Do you have any sort of DDOS protection/bot traffic filtering like using Cloudflare or similar?
It seems like most errors I get these days are from ridiculous amounts of automated traffic that comes in large bursts and I'm wondering if it's affecting your forum in a similar way. The reason I ask is because at least one of the example errors you posted had what looked like a spam thread title in it.