I found it with Google.
In retrospect I should have been able to find it myself by searching the Minecraft directory.
So 1.6 saved the chat contents in a file named "output-client.log" does 1.16 save chat anywhere?
Or is there any way to save it? Or at least cut and paste it?
Preferably a lot more than just the last 100 messages.
This is in single player btw.