Can you host a minecraft server on github?
It is possible to run a Minecraft server on GitHub Codespaces. However, you need to set up the Fabric server jar as you normally would but on the codespace and start the server. Once the server is started, copy the IP shown under Forwarding (minus the tcp://part and including the port) to connect to it. Note that there are limitations with using free versions of services like ngrok and GitHub Codespaces.
You mentioned limitations, are there any that I should know of?
GitHub Codespaces is a cloud-based development environment available to all GitHub Free and Pro accounts. However, the free tier has limitations:

1. Free plan account users get 120 core hours and 15 GB of storage per month.
2. Pro accounts get 180 core hours and 20 GB of storage per month.
3. Exceeding the included usage will result in additional charges.
4. Users can set up a spending limit to keep working and track usage on their billing page.

I hope this answered your question. Please let me know if there are any other queries you have for me.