Forgejo is a great fit for what you're describing. I run Fjord, which is managed Forgejo. Our dedicated instances are above your $5-10 budget, but we also run a free public Forgejo instance if you want to try it without operating anything yourself.
Forgejo has been great for me too. I liked it so much, I added a feature to make it relatively easy to get up and running on exe.dev. Support for Gitea and Tangle.org is also available.
