To complete this thread, I am posting the response from Odoo via the ticket that I logged:

Pulling the Odoo source code *never* requires any module to be upgraded to avoid crashes - that's the entire point of our stable policy.

Basically, 3 types of files can be changed in a bugfix:
- Python files (e.g. method changes, etc. without any database model change - server restart is sufficient)
- JS Files (server restart is sufficient to trigger assets minification etc.)
- XML Files (module upgrade usually necessary to enjoy the fix but not doing so will not cause any error)

Since the error does not append anymore, it's basically impossible to say what exactly happened in your case. However the issue is clearly on the JS side; one culprit could simply be that the assets you had in your browser cache were no longer matching the latest from the server (this is in practice unverifiable).  In any case, a module update for a JS error is never needed (it's a canon to kill a fly as we say in French); your module update fixed the problem (most probably) by regenerating the assets but that's more of a side effect.

Regarding your best practices, there is nothing to do on your end; the code gets update every monday and odoo.sh instances restart regularly by themselves after some inactivity. The whole point of Odoo.sh is that you should *not* worry about this; it seems you had an unfortunate experience that, understandably, erroded your trust a bit.

Since I cannot inspect the matter at this time, I'm afraid you can only take my word for it - should the problem happen again in the future, do not hesitate to switch to the 'assets' debug mode where Javascript files are not minified, which make the traceback possible to analyse (by appending ?debug=assets after the /web url). As it is, I'm afraid there's nothing more we can do.

My conclusion
The management of updates to Odoo.sh matches my expectations and I am happy with the information I received from Odoo.  I have had no further issues from this particular database, and none of our other databases (dozens) hosted on Odoo.sh were affected.  At this point, I believe it was just a glitch and have moved on since there is no way to determine what actually happened.