Sidekiq boot loop after upgrade

After last upgrade to 14.6.2 (from 14.5.x), the sidekiq service stopped working on my self-managed instance (omnibus):

Checking Sidekiq ...

Sidekiq: ... Running? ... no
  Try fixing it:
  sudo -u git -H RAILS_ENV=production bin/background_jobs start
  For more information see:
  doc/install/ in section "Install Init Script"
  see log/sidekiq.log for possible errors
  Please fix the error above and rerun the checks.

Checking Sidekiq ... Finished

Taling the logs shows that sidekiq boots up and then shuts down continuously:

/var/log/gitlab/sidekiq# tail -f current
{"severity":"INFO","time":"2022-01-14T12:35:25.747Z","message":"A worker terminated, shutting down the cluster"}
{"severity":"INFO","time":"2022-01-14T12:35:26.545Z","message":"Starting cluster with 1 processes"}