https://docs.github.com/en/rest/migrations/orgs#start-an-org...
https://docs.github.com/en/rest/migrations/orgs#download-an-...
Using a Github App you get 15K requests per hour. Even with pagination(100 records per request) you should be able to get at all of this data within a couple of hours. I suspect you lack reliable transformation tools to take github metadata and convert it to gitea versus the limitations of GitHub.