The matrix core team was very much long-time IRCers (opering networks since late-90s) before we embarked on Matrix, so we've tried to make it a decent transition. The python weechat-matrix plugin is pretty good (in my opinion, although others seem to have had bad experiences). Matrix itself stores your conversation history for you, so most people don't bother storing separate logs. There are tools to let you maintain separate logs though, e.g. https://github.com/russelldavies/matrix-archive - and log export is also currently being added to Element.