I passed by the pretty Kaltengrundsee in Bavaria (Germany) and it looks inviting to take a dip when the weather is hot. There's even a platform to get in or out of the water.
Source: Wikimedia Commons
However, it's also classified as a Naturdenkmal (natural monument).
Is there anything in the status of this lake as a Naturdenkmal that restricts the access rights for wild swimming?
Art. 9 BayNatSchG – Naturdenkmäler says:
[...]
(3) Naturdenkmäler werden durch Rechtsverordnung unter Schutz gestellt.
(4) Vorbehaltlich einer anderweitigen Regelung in der Rechtsverordnung ist es verboten, ein Naturdenkmal zu entfernen, zu zerstören, zu beschädigen oder zu verändern; die Handlungen, die mit Geldbuße bedroht werden sollen, sind in der Rechtsverordnung nach Abs. 3 zu nennen.
[..] which deepl translator translates as:
[...]
(3) Natural monuments shall be placed under protection by ordinance.
(4) Unless otherwise provided for in the ordinance, it is prohibited to remove, destroy, damage or alter a natural monument; the acts which are to be punished with a fine shall be specified in the ordinance referred to in paragraph 3.
[...]
... which I read as meaning that there are no further automatic restrictions than the ones listed above. Any further restrictions such as no swimming or do not leave the official paths would likely be possible, but they also need to be posted.
I clicked into the ordnance for some other Naturdenkmal, and that had the level of no camping, no picking of plants, no building nor destroying of [further] paths or platforms etc, but not even the level of "keep on the official paths". And that is in accordance with e.g. the Eschbacher Klippen being a rock natural monument, and it is perfectly fine to walk up or climb them (magnesia/climber's chalk is prohibited, though). In analogy, if the monument is a lake, and you can go swimming without destroying the vegetation I'd expect you can swim as long as there is no sign that says "no swimming".
