Just wanted to say this was exactly as I experienced when I first set up my site (so its not unique to your site).
Heres a thread I made about it at the time:
This is what caused me to jump up different CPU/Memory options outlined here
Unfortunately, I have not had a chance to properly swap to Hetzner from Digital ocean as I described (started a new job). But will do as soon as I get a chance this month.
The end-user experience of being kicked out of the thread, or remaining in the thread (with the logged our message). Did seem to correlation dependent on load. (more users were sent to site index after a goal scored)
I don’t have enough technical knowledge to be helpful, but felt it might help to know a sporting site with similar peaks of chat like behaviour does lead to a similar issue. But mine (smaller, and younger site) was resolved by further upgrading server.