I replaced the carpet on our old Winne a few years ago. NOT a fun job, but do-able. And yes, the carpet is supposed to be under this particular setup.
What spdracr39 said, the new wood on the main floor has to match original thickness. When the guy put new wood floor in our old Monaco, seems he had to adjust the height somehow to compensate for slightly thicker flooring, but I don't know how he did that.
With slide out, look under from outside, you can see where that outside end is attached. Seems there was a strip of (metal?) with screws thru it, and plenty adhesive so it is stuck pretty good.The carpet has to go all the way back to the outside on the underside, else it will catch when you run the slide out, thus the carpet wrapped all the way around. Get that old stuff off than proceed. That oscillating cutter should help, and several (expletive deleted
) comments to encourage the team.
With the slide IN, you can tilt the top back out, allowing you to get at the bottom of the slide, and it seems we used some 2x4 scraps under it to give a bit more clearance, otherwise there is almost no space to work in.
Start from the Outside bottom with the slide out when installing the new stuff. Slide the carpet under from inside, than fasten it securely on that outside end. You will need a second set of hands here. I found some REAlly sticky tape to help hold the new carpet, Capitol Grip double face adhesive tape, great stuff; and be sure to get all those fasteners back in, you don't want that stuff coming loose under there. A rubber mallet and a wood block worked great to help set that carpet into the adhesive and make the bend as you fold it around. I used my air powered crown stapler too.
When we got done, it was great! The professional carpet installer said what he mostly learned was, this was his first, and LAST, recarpeting job in an RV!!
If you are not going to put carpet back on, no idea how to fix that. Perhaps install the carpet up to the top of the facia, and find some sort of strip to help hold it in place. Maybe the adhesive and LOTS of staples will do it, not sure. If that facia is metal maybe a strip of metal with screws will work?
Good luck