I’d appreciate any thoughts from the generous Forum experts on our permit situation.

We’re considering moving from Romandie to a Swiss-German canton, mainly to experience life in a new part of the country. But we are unsure how this would affect our permits, since:
1) I’m a UK citizen with a B-permit (pre-Brexit – valid throughout Switzerland for >2 more years). But I recently left my job and am not currently employed.
2) My spouse is a non-EU citizen who joined me on a family reunification permit WITH the right to work. This permit is only valid in our current canton and requires re-applying if we move to another canton. She is employed in a "field" position by a Swiss company.

The question is whether moving cantons in our current situation will cause problems with either (or both) of our permits. Is re-application generally smooth for someone already employed? Will my current jobless status impact my permit or my spouse’s? Does the answer vary by canton? Any insights very gratefully received.