You cannot do it using standard approach with personal access tokens (PAT) but GitHub offers amazing workaround which allows you to accomplish it.
First of all, you need to create app using this guide which is little bit unclear about Installation ID.
There is a simple way to get it from page's URL. We need to open organisation where we've installed this app then open Settings and then open:
npx github-app-installation-token --appId AAA --installationId XXX --privateKeyLocation ~/key.pem
After getting key we can authenticate with this token using GitHub cli tool:
gh auth login
What account do you want to log into? GitHub.com
What is your preferred protocol for Git operations? HTTPS
Authenticate Git with your GitHub credentials? No
How would you like to authenticate GitHub CLI? Paste an authentication token
And after that you can do any required commands on specific repo like creation of new release:
gh api --method POST -H "Accept: application/vnd.github.v3+json" /repos/<org_name>/<repo_name/releases -f tag_name='v1.0.0' -f target_commitish='main' -f name='New Fancy Release'