As noted in a previous answer by @OOPer, you probably want not to change your password, but instead generate a "personal access token." I don't know about previous versions, but in Xcode 13.3.1, the prompts indicate that reasonably well. One of the prompts links to GitHub's instructions on creating a personal access token (https://docs.github.com/en/authentication/keeping-your-account-and-data-secure/creating-a-personal-access-token).
As of July 2021, personal access tokens can now expire. (https://github.blog/changelog/2021-07-26-expiration-options-for-personal-access-tokens/) You can still set your token not to expire, but they "strongly recommend" against that. You can set the expiration up to 1 year (via "custom" date).
When your token expires, GitHub will email you with a link to GitHub's site to regenerate the token. You can also do that from GitHub's site by going to the "Personal Access Token" section -> click on the token name -> "Regenerate token."