I dont know about caddy but nginx proxy manager does this very well. Also, if running in docker, you can expose the port that runs ssh for forgejo und a different port than the host machine‘s (eg 2222). In that case you just put the remote in with the port and call it a day.
Strongly agree! I switched as well, so did my wife and its glorious. We‘re both avid gamers and no issues so far. We have strong opinions about intrusive anti cheat software so that helped.
I did make a windows vm for my wife since she needs to work with adobe sometimes and it seems to work perfectly so far.
Feel free to update on your journey.