Just to add to the fray, here's what I've found:

• Forgejo - install on a PC at home - works well, but you can't easily share your code with people outside your home. (https://forgejo.org)

• Codeberg - runs Forgejo under the hood - now you can share with people - but you really ought to donate to them if you use their service. (https://codeberg.org)

• PikaPods - will host a Gitea instance for you in their cloud - you can share code this way too - costs about $2 USD per month and is dead simple to set up. (https://www.pikapods.com/apps)

• VPS - go set up your own virtual private server (on a free Oracle server, or other various hosts out there) and install Forgejo on that - more complicated, hope you like securing servers - share as you like. Free or maybe $$$.

Have fun!