SDK_INT 24 and RELEASE 7.0 means… Android 7 and not 13… 
and yes, on 7 it’s complicated, on 6 and lower the certificate fixes it, on 7.1 or later it’s fine
but 7.0 … do try to pull-to-refresh every 16 seconds so maybe a mirror with the right cert can be used, it might take longer but there’s a bigger chance
I have noticed it lying about the availabe storage space.
It says, there is 256 GB.
But about, when the used storage should be about 16 GB,
it starts to claim, I have already used up 255 or 256 GB.
The sum of the itemized list of used storage however is always orders of magnitude less.
Perhaps it is also lying about the android version in the settings. (?)
SECURITY PATCH 2017—? Android version history - Wikipedia
Thank you @vdbhb59
I can apparently indeed get the text that way.
In the settings, it says, the security updates are of April 5, 2023.
it can say anything there, but if you get the certificate error… that’s a lie 
Anyway read Let’s Encrypt ISRG Root X1 and Privacy Browser – Stoutner and add the certificate, restart, retry…
I had allready tried pull-to-refresh to the extreeme.
Each “update” took some time.
But I never got any results from those, but error messages.
I will try your suggestion @Licaon_Kter , but it will probably take me som time to read, understand and apply.
It was easier, than I anticipated to install that certificate.
I downloaded it with wget and renamed it (removed the .txt) using termux.
I selected to install it.
I was forced to set id or pattern for login or whatever.
Then it was installed as a user certificate already.
Now, I found, that the index update took longer and did not produce an error message.
Instead I did get the list of the apps.
I reactivated the entry mentioned to be deactivated above
and the update still seemed to be working.
I did not see entries related to the original problem in the debug log this time.
That problem did not seem to affect the web browser, that came with the tablett - when visitig https sites.
F.e. I could also vist that test site from lets encrypt without problems - before I had installed that certificate.
But apparently, that cert was not installed among my system certs
and I did need it for the f-droid client app on this tablett.
long text, so, success or not? 
Success
Thanks all your help!
Of course, now I am confused about what version of android I really have on this device… 
that’s great you fixed it!
For other people with similar problem of unfixable HTTS certificates in F-droid in the future, one workaround might be to not use HTTPs at all-- instead, install ORBot, enable TOR in F-droid settings, and enable only HTTP Onion services mirrors (i.e. http://*.onion URLs) - the transaction integrity will be provided by TOR instead of HTTPS then
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