Silly of me. I forgot about the very clever and granular way that CiviCRM is built. Just creating a new Activity Type was not enough to have it activated in the right CiviCase.
After creating a new Activity Type (either Task or Communication), we must add these new Activities to the right Case Type that can be customised.
And voilà, it's set !
At this link it says send an email to email@example.com: https://civicrm.org/about/core-team
It also says you can hire any of the experts.
On the particular civicase issue there are a couple tangled up issues with closed cases (https://lab.civicrm.org/dev/core/-/issues/1401) but maybe this one (which is listed in there) could be dealt with without getting too ...
At administer - civicase - civicase settings there's a setting for Enable Embedded Activity Revisions. The civicase extension suggests turning that off and instead using administer - system settings - misc - logging.
Migrating 10 log records probably isn't worth it, and the revisions setting hasn't worked properly in the UI for a few years now anyway so you ...