Thanks for the file, nose-show (No idea either, but you can change that)

The IK chain that you have set up misses the Pole, which can be used to rotate the Chain. The Target (Ziel) is the main object to move anything besides the Pole in IK mode. The Joints are not touched when in IK mode.

If you want to rotate the joints, go into the IK tag and use the IK/FB slider to move it to the right to be out of IK and entirely in FK. Now you can rotate the Joints individually.
Invert kinematic and Forward Kinematic in opposite directions.
The algorithm finds the best solution in IK mode based on the Pole and Goal. Any other influence will create, more or less, chaos.

I would not use the Protection Tags in such a chain.

https://help.maxon.net/c4d/2024/de-de/Default.htm#html/TCAIK-ID_TAGPROPERTIES.html?TocPath=Object%2520Manager%257CTags%2520Menu%257CRigging%2520Tags%257CIK%257C_____2

As a side note, the Group Nulls under each Joint is not centered on the Joint. Otherwise, this Null could be used to rotate the element; of course, it would not affect the ones below, and that would be another step.

All the best