If I may speculate . . . This is not my specialty, and I tend to get all confused when folks start talking about “floating neutrals” and such. Let’s look at my understanding of how things work.
It’s my view that electricity “works” by being able to get back to where it was “born.” That is, back to the transformer at generator where it originated. It seems to me that this is the ONLY place the neutral needs to go; the electricity doesn’t want to go anywhere else.
As for the “grounds,” I see grounding to serve two purposes.

Purpose #1 is to collect any electricity that “leaks” or “gets lost” and return that electricity to its “home.” That is, the generator or transformer where it was made. It is by having a good, solid return path that the fuses and breakers work. So your green wires, etc., need to have a good path back to your generator. I’m not sure that relying on the bonding of enclosures is reliable enough - there ought to be a real wire between your panel and the generator.

Purpose #2 is to give static electricity (read “lightning”) a way to return to Mother Earth without burning up everything in the house. For that you need a good, solid path from your panel into the ground itself. This path has nothing to do with your generator. I see generators with connection points for running a wire to a rod (or other electrode) and I wonder what’s the point? Lightning is going to hit the building, not the generator — and the little ground wire in the generator cord isn’t going to help much!

This leaves the question: When we use the generator, what do we do about the neutral connection to the utility? I suppose it’s better to separate your system completely from the PoCo grid, if for no other reason that you’ve lost power because something has gone wrong on the PoCo side, and you don’t want anything to do with them until they get their stuff fixed. Do transfer switches typically also switch the neutral?

Just what, I ask, is a “floating neutral?” If by that you mean that any voltage applies to the ground wires and conduit has no place to go, no path back to the neutral terminal on the generator . . . I say that’s a very bad idea. Without such a path there’s no way for the breakers to clear faults.

Am I missing something?