Have you been able to pull the dash switch to check wiring there?
they no longer are posting the actual 12VDc wiring schematics so we are limited toguessing how things like this are built. As they are going through the drawings and switching to far less useful info we are gradually losing the info we need to be able to sort trouble with any real good plan!
But if you are able to get the dash switch out, there may be some ideas that help?
I have not looked at one anywhere near the 2022 year model but I might guess the switch will have six lugs on the back for choosing which power. The center two lugs would be expected to go to the radio, with one set of outer lugs feeding power from coach and the other from the chassis.
What I expect to find is a switch that connects battery and ground from the coach on one set of two outer lugs to the center pair, then when we flip the switch the other way, those two center lugs get connected to the second set of outer lugs. Double pole, double throw (DPDT) meaning two lugs (poles) can be thrown two directions?
If you can get the switch out to access the lugs, I might suggest looking for battery and ground from the coach on one set of two lugs as it seems to work.
Then when that is ID'd, look at the other end of the switch for the other two outer lugs for battery and ground from the chassis?
This IS getting pretty deep in guessing without having actual info to follow, so be aware of flaws in the plan?? Theory based on the way I have seen it done in other places?
But what sounds correct is that you have battery and ground getting from coach to outer lugs and then the switch connects it through to center lugs to saend on to radio!
The fault may be in the switch not connected it through when flipped (defectiver switch?) OR the feed bring power from chassis battery point to switch may have a problem.
If you find the Winnebago wires have ID stamped as the last 2-3 letters in a long chain on the wires, it may be possible to look up that ID on this list to find the "from" and "to" of that wire.That can lead to knowing if it is battery or ground?
Something like this could help to sort?
Shows wire LS is 12 gauge yellow wire feeding coach power? But where is chassis and is it labeled for ID?
Is it switch defective or is it a chassis problem as simple as a fuse tripped in some spot we have not looked?
Possibly checking any fuse box where you have chassis fuses might lead to finding one blown as the more quick and easy thought?
Got any drawings on hand for chassis info in the big bag of info? Maybe a handy label inside a fuse box under the hood?
Lacking info it is getting very hard to solve some of these questions and they are going through the online drawings and reducing the help we have had in the past!

Wish you luck on the chase!