My upgrade process:

I setup upgrade channel BETA

Uninstall modules that I currently do not use, including the Czech Language module that I created and set the default language English

Site settings-Enable auto-update and Force auto-update, even if some files were modified

Clear all caches then i start Update according to Alex T instructions.

I always waited for confirmation to come to my email after the automatic module update,then I checked again whether there were any other updates and installed them if necessary.

The last email confirmation is: 

Last update from 13.0.0-B3 to 13.0.0-B4

Albums module: up to 13.0.3 version. Conversations module: up to 13.0.3 version. Decorous module: up to 13.0.6 version. Developer module: up to 13.0.3 version. Discussions module: up to 13.0.6 version. English module: up to 13.0.5 version. Files module: up to 13.0.5 version. Groups module: up to 13.0.4 version. Invitations module: up to 13.0.3 version. Lucid module: up to 13.0.6 version. Nexus module: up to 13.0.3 version. Notifications module: up to 13.0.4 version. Paid Levels module: up to 13.0.1 version. Persons module: up to 13.0.5 version. Protean module: up to 13.0.5 version. SMTP Mailer module: up to 13.0.1 version. Timeline module: up to 13.0.5 version.

Unfortunately after this upgrade the site is again broken.Database query error!

I overlooked something somewhere or set it wrong, so hopefully this will help to solve it.

I haven't been able to get any further yet.

The upgrade and upgrade modules logs are attached.