I have generated classic token in GH: github-api-access with admin:org_hook scope and used in GitHub Server section in Jenkins -> Manage Jenkins -> System. Test connection shows me:

Credentials verified for user user_name, rate limit: 4998

Probably that's not enough because I reached my limit after a few days. If I click on Re-register hooks for all jobs I see Called re-register hooks for 17007 items.

For example for Github App token I have: Success, Remaining rate limit: 14998
I'm looking, why after upgrade jenkins and plugins a hook from GH does not invoke a Jenkins build. 
Previously I used jenkins 2.504.3 and plugin 1.43.0 - outdated, the problem was incorrect project configuration. The only question that remains is the limit.