Perhaps I was a little imprecise, so allow me to clarify.
The focal length doesn't change when a lens is moved over from DX to FX. However, depending on the lens design *and* interaction camera-lens, the covered area can change or image resolution might suffer.
Some DX lenses trigger the target camera to set it self to a DX frame, for example, my Viltrox lenses for Z fc on the Z9. They thus will keep their focal length (of course) *and* their angle of view, but the camera resolution is lowered, in the case of Z9, from 45 to 19Mpix. The Voigtländer 35mm f/1.2 DX does not interact in this manner and if the camera is set to FX, it will remain so. However, the projected image doesn't fully cover the FX sensor area and hence strong vignetting occur. IF the Z9 is manually set to DX format, the Voigtländer 35 behaves as it does on the Z fc, and the slight drop of resolution from 20.9 MPix (DX, Z fc) to 19 (DX, Z9) is hardly significant.
In practice I swap my Viltrox lenses between Z/DX and Z/FX (Z9) cameras without any mental efforts. The lower file size on the Z9 rarely is important as resolution by and large remains the same in this case.