If you scroll down to the Features section on the linked page that gives a good overview.
In hexchat GUI client chat history is locally found in a simple text file, one line per message in .config/hexchat/logs/irc.libera.chat/xxx.log
However I've found no option to create such a log with halloy, am I missing something in the documentation?
If you scroll down to the Features section on the linked page that gives a good overview.