Crop mode in the R5 and R6 is used to achieve the same FoV as one would get using an APS-C sensor camera. It is necessary if someone like yourself is proposing to use an EF-S lens via an adaptor on the R-series FF bodies.
On EOS DLSRs this was not possible because the lens reaches far into the body and, on a FF camera, will impinge on the physical space used up by the mirror as it flips up. With the MILCs and an adaptor that distance is no longer an issue, but the lens optics are not designed to give full coverage to a FF sensor, so the images would have significant black vignetting if the image was not cropped by the camera software. This is done automatically in the later R-series camera bodies.
In your case, we come to a challenge that exactly ties to my whole issue of understanding FoV, cropping and pixel density! You apparently have EF-S lenses designed specifically for APS-C bodies, and the R series cameras will allow those lenses to be used, but at a much reduced resolution. So, if you really want the benefit of the 20MP of your camera, you need to get lenses designed for a FF unit. You could get an EF-L unit and use it with an adaptor - there are a lot of bargains to be had in that space as a constituency of photographers turn over their EF lenses for the new RF ones. Yet, a good lens is a good lens! I have shot with the following EF lenses on my R6 bodies: Canon - EF 24-105L f/4 MkI, 70-200 f/2.8L IS USM MkII, 100-400L IS USM MkII, all three EF 70-300 units; Sigma - 150-600c and 60-600s lenses. They have all worked flawlessly.
Depending upon your needs and the budget - I don't recall you saying exactly what focal ranges you want to work within, the RF 24-240 lens is a bargain: admittedly, it's not weather sealed, but it delivers stunning images for the type of unit it is, and again, depending upon what you produce, it might suit your purposes. Your R6 will do a lot of image correction in-camera to the viewfinder, and with the JPG files; and bringing RAW images into PS or LR should apply auto correction for vignetting and chromatic aberration, both of which look horrific without those. This lens is an extreme expression of a trend in lenses these days, a degree of optical performance, but combined with significant image correction in firmware (in camera) or software (in PP). Basically, I think we are at last seeing the benefits of computational imaging, long used for cell phones, arriving in camera optics.
I also use the RF 24-105L f/4 and 100-500L units and they are both brilliant lenses, yet the 24-105 is not significantly better than the 24-240 after processing, oddly enough - although it has a constant aperture and is weather-sealed.
If searched in my archives and found a couple of images taken with the RF 24-240 and RF 100-500 FWIW, but bear in mind that the quality has been much reduced to fit into the 5MP limit for posting to this site.
Details: Canon EOS R6, RF 24-240 IS USM, 230mm, f/6.3, 1/120sec, ISO-3600, hand-held
Canon EOS R6, RF 100-500L IS USM @500mm, f/7.1, 1/500sec, ISO-640, Hand-held
