All my base are belong to me! (For young people, that indicates success)
1) Factory reset did restore the IPv6 tab, but that might not even be needed, because...
2) After editing .export config file (ipv6_hidden = no;) and recalculating the checksum (https://github.com/mementum/fritzchecksum) I got my config back, while still having the IPv6 tab enabled.
Unfortunately, I was not able to figure out what setting is enforcing "Allow automatic configuration by the internet provider" (TR-069) so that one is still enabled and still grayed out. Hopefully long hand of 2degrees will not find me here...
Unfortunately I was not able to get IPv6 address with Native IPv6 method, and only got one with "Use IPv6 with a tunnel protocol" and "6to4"... so not sure if this is of any benefit or should I just keep it off?
Thanks for all the clues!
Andrej