Some background:
As Germay is a federal state, there are 16 different laws that regulate where you are allowed to dive on puplic grounds.
If the dive site is privately owend, the "my house, my rules" applies. As they are liable if something happens, they usually require a cert and a medical self statement; there are also some that are more or less "open" and no checks are done. Some of the more advanced sites have even banned certain certification agencies due to a lack in trust that the education is good enough.
On public land, it's either "dive unless forbidden" or "no dive unless allowed"; Bavaria falls into the later. Two of the best lakes in Bavaria (Starnberger See East and Walchensee) are even more complicated, as different dive sites have different rules and access by car is restricted.
If you join a dive center for one of their outings, it again comes down to liability, so they need to check if you are fit do dive. If you go diving on your own, there is even no requirement to have any kind of certification at all
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As for Austria, again there is a difference between privately owned and public land. Blindsee for example charges an etry fee, Fernsteinsee (and the most beautifull Sameranger See) require you to stay 2 nights minimum at their hotel and you have to have proof of a certain amount of dives.
The lakes under control of the ÖBF require a DiveCard to be bought and adhere to certain rules.
"It's complicated" is an understatement