There appears to be an issue with the composer package registry. I was able to upload the file using the documented curl command and it was able to parse the contained composer.json file for the name and version.
When trying to access the package through the web interface to assign it to a repository, I get a 404 error. The URL structure is as follows:
https://{hostname}/{owner}/-/packages/composer/{vendor-name}%2F{package-name}/{version number}
It appears to have issues with the slash between vendor and package names but this is the naming convention for composer packages.
Gitea version 1.24.7 via Docker Compose with a mostly default configuration.