Verified on Satellite 6.10.4 sn 2, satellite-maintain health check now deletes paused tasks as expected and CV publish tasks can be successfully triggered afterwards.
Since the problem described in this bug report should be resolved in a recent advisory, it has been closed with a resolution of ERRATA. For information on the advisory (Satellite Maintenance 6.10.4 Async Bug Fix Update), and where to find the updated files, follow the link below. If the solution does not work for you, open a new bug report. https://access.redhat.com/errata/RHBA-2022:1115