It’s free to expect something, but they didn’t note any fix about that (although beta changelogs are not disclosed recently) so don’t expect much. 
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There is no official answer to the question. Avast employees ignored it, as usual.
There seems to be no way of exempting specific websites from HTTPS scanning by contacting Avast s.r.o., although the whitelist still exists. See this reply.
The warning message seems to be a bug, the existence of the whitelist today may be another bug.
I have written a “solution” to my original question.
The proper place of our discussion would have been my other post. I have summarized our findings there. If anybody has something more to say about this, please continue under that post.
Thank you for the contributions.
Update on this: With Avast 24.12.9725a (build 24.12.9725.897) and Firefox 133.0.3 (64-bit),
I have re-checked the bank websites I previously listed, that had the “not recognized by Mozilla” padlock indication.
None of them now do that for me anymore.
Thank you for the feedback.
I have turned on my computer, visited this forum, and checked the 5 UK bank websites, you cited. All of them worked. After that I did my steps to reproduce, and the sites showed the warning message in the 2nd run. After this I retried the 5 UK bank websites, and all showed the warning message.
Avast Free Antivirus 24.12.6142a (build 24.12.9725.897).
Firefox 133.0.3 (64-bit).
Avast has two versioning schemes. I have the other, but the build number is the same as yours, therefore it is supposedly built from the same code. The same program has different behavior. How can that be?
What a difference a day makes.
@PaulBlueberry you are correct all the UK bank websites I listed are today again showing the “not recognised by Mozilla” indication. 
EDIT:
It is all seems random, as now (a couple of hours later) certificates read correct again.
I give up.
Thank you for the update.
I suppose, it doesn’t depend on the time, when you access the websites, but rather the number of HTTPS sites you opened since computer start. If I’m correct, when you don’t see the bug, you just started the computer some minutes ago.
If, however, you don’t see the bug, and you do the steps to reproduce, you will see the bug.
Correct. It is OK at first, then seems to occur after browser used opening different HTTPS pages.