Yes indeed, your Insta360 ace pro doesn't work with the Hohem Stady Pro 4 stabiliser, on the product description it says which headsets should be compatible.
I have a DJ-OSMO ACTION, it's compatible in terms of its shape but not for triggering recording from the control handle, but it's still pleasant to use and the images are still very fluid when moving from different angles.
Personally, I use it for sports rushes and it works very well.

No