I had to reset all my tokens for Github recently because I’m dumb and accidentally pushed one to a code repository.
This broke HACS on my Home Assistant install because the token wasn’t working and rather than gracefully handle that, or make it possible for users to re-enter it, it just dies.
What I found is that you really should remove the HACS integration, restart HA and re-add the integration, which will prompt you to do the “Github Device” setup
If you do want to continue to use the Personal Access Token (PAT), I was able to find it on the filesystem in /usr/share/hassio/homeassistant/.storage/core.config_entries which seems to have a lot of unencrypted stuff. Ergh.
Look for the section with HACS and something like this:
"title": "HACS",
"data": {
"token" : "<your old token here>"
}
Edit the token value, save the file and restart HA Core. It should figure itself out.