An APS-C lens or a full-frame lens instead?

With Canon, the choice of EF-S and RF-S lenses is very limited, so you'll still have to choose an EF or an RF lens.

I also have an APS-C camera myself, and most of my lenses are also for the APS-C camera. But I also still have enough FF lenses, which I use very regularly.
For me, it therefore doesn't matter which lenses I have, as long as I can take photos with them.

Interesting question. But not entirely relevant. If you want a wide angle on a Dx camera, you actually can't use an Fx lens, it tops out at 11 mm, and is suddenly bulky, large and heavy. On the other hand, telephoto lenses make no difference at all, an f4 600mm is exactly the same size for Dx as vor Dx, you can of course choose a 2.8 400, but your back won't be any happier with that either.
So the story is about a small group of lenses around the standard focal length, 16-80 for Dx, 24-80 for Fx, and then you immediately see where the problem is, that Fx has a much smaller range. Wide-angle zooms are the same.
So technically speaking, it is a non-issue, a Dx lens on Dx, until you get into the telephoto sector, for Dx there is no choice.

Then I set my full-frame sensor to crop. The other way around doesn't work.

That is almost always the case but not always E.g. Tokina 12-24 from 18 mm works fine on full-frame and the 11-16 can be used at 16 mm, also Sigma 10-20 f3.5 and the Nikkor 12-24 from 18mm. Up to about 24 megapixels reasonably good to good sharpness and ok vignetting in the corners. These are lenses for DSLR. And there are more like that. Note many Sigma Art lenses have deliberately been given a larger image circle, also the Tamron 15-30mm and work fine on large-format Fuji GFX. You have to look at each lens individually. If you trade in your APS-C, quickly test in the shop whether your lens works. That's how I kept my 12-24 Tokina, used it from D200 on my Nikon D800 and still on full-frame film instead of Nikkor 20mm f2.8 .