I reported that bug on 8 December 2019 - https://github.com/BOINC/boinc/issues/3397

They were aware of it even before I posted, but there's a huge re-write going on - expect it to be a while yet.

7.16.5 is still available on APKpure website and app, it fixes one of those bugs, but has some other different bugs.

Importantly, 7.16.5 still has the Certificate error.

... Anyway, why can't I get to LHC with 7.16.3?

YOU CAN'T!
Currently there is NO Android Version available to download / install with a FIXED Security Certificate.

LHC has to FIX (remove / replace) the security certificate(s) issue that has been noted HERE on the BOINC message board on THEIR SERVER like ROSETTA has apparently done.

I don't know how I got 7.16.5 ..,

If I recall, it was available in the Google Play Store for a short while before it was removed and also the "APK Program File" was available to download from the BOINC download area for about the same time.

So what was the 7.16.3 release intended to do?

See post 98786 where Jord replied to a previous inquiry YOU had made about that version.

7.16.3 was a beta version, it never made it to a recommended version for any of the platforms due to bugs. So when the decision was made to not support 32bit Windows any further, it was easier to keep the working 7.14.2 as the default version for 32bit Windows and go with 7.16.5 for 64bit Windows.

On older phones, running older Android versions, you might see older versions of the client. Like Android 4.4.1, 6.0, etc...