Hi Guys,
I solved the problem.
I had to delete these extensions via command line. That was the case, for example.
php56 composer.phar remove davis/flarum-ext-customfooter
php56 composer.phar remove davis/flarum-ext-customheader
I did not expect this, but after I deleted the obsolete extension "flarum tags", the new Beta 6 extension for Flarum tags had dived and my old tags have been preserved. Very cool and helpful.
Now, in hindsight, I know that I had to disable all extensions, which are not part of the Flarum Core, before upgrading to Beta 6.
Problem solved, I would say.
Also, you can remove the enabled extensions in the table "settings" in the flarum database. Then they are at least not activated. The deletion of an old extension functioned with me only via command line.
Thank you for the tips and hints.