My issue was having a .gitconfig file containing an insteadOf URL directive. After commenting out the lines in the gitconfig, Xcode 13 accepts the GitHub personal access token.

On 14.2: It kept looping Resolving Package Graph and Packages for me as well. Cleaning the Local Package Cache showed an error with a local git repository: it its .git folder was corrupted. But didn't fix the looping issue. Removing the Playground from the Workspace fixed the issue. Ah nvm.. it started again. The freezes every couple seconds are the worst.

Recreating the workspace fixed it.. for now.