About parent-child movement by transform.SetParent of charactercontroller object

SetParent" to move the parent and child of the object without a charactercontroller, but if a charactercontroller is attached to the object, the object falls without moving the parent and child.
However, if a charactercontroller is attached to the object, the object will not move and will fall.
This is an addendum.
I recreated a new project with the minimum configuration. The parts I was using are still there.
I have zipped the project file in the following page. If you can take a look at it, please let me know.

https://firestorage.jp/download/483c6e64f7fc36f536d971df2f2ca914e4b77e59

SetParent does NOT move anything. It changes the Transform relationship between two Transforms.

How about instead you supply a link to the Unity documentation explaining how this setup SHOULD work, and then explain how your experience differs from what the documentation promises?

A diagram showing transform hierarchies might be useful in this case, as well as any other descriptive illustrations.

Thanks Kurt-Dekker!
I’m so thrilled to be following you again!
I tried a few more things, and managed to solve the problem successfully by not using the parent-child relationship.
Thank you again!