Why is the recommended release of my module not proposed in Drupal updates?
Immediately after posting my question, I'd pushed a new 7.x-2.2 release, and it didn't change anything: all involved sites keeped reporting 7.x-2.0 as the most recent release.

But today I noticed that it suddenly changed (without any intervention in git nor in my module's page): now the sites correctly report 7.x-2.2 as the most recent release.

So I tend to think that the response to my question is merely: there is some variable latency in the way Drupal.org makes the information available for the admin/reports/updates/check page underlying mechanism to work.

Moreover it worth mention that also the git Age list now shows all release tags, while some of them were previously missing.