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
What's a crop mode?
Assuming that you are asking specifically about the crop mode on an R6;
As Tronhard explained in detail:
"In your case we come to a challenge. You apparently have APS-C lenses and the camera 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."
More specifically, in "FF Mode" the R6 sensor actually covers an optical area of 23.9 mm High X 35.9 mm Wide which is nearly the size of a full frame of 35 mm film (24 X 36 mm). Given the pixel density of the R6 sensor, that equates to an usable digital image of 19.96 Mpix. (3648 X 5472 pixels). To optically cover that sensor area requires a Canon EF or equivalent lens.
When an EFS lens (with its smaller circle of illumination) is mounted using an adapter, the camera is automatically switched to "Crop Mode". That reduces the usable part of the sensor to the central 14.86 mm H X 22.36 mm W imaging area or 2272 X 3408 pixels. This sensor area is commonly called "APS-C"; the area the EFS lens was designed to cover. You now have a 7.74 Mpix R6 Camera. Think slightly less than a EOS 30D. Obviously, the reduced sampling resolution will limit the maximum usable final image size (probably to no larger than 11X14 inches without visable sampling artifacts) and will limit the amount of any post cropping possible.
"Full-Frame" cameras need EF lenses. Allowing the use of "APS-C" lenses is fine as long as you are well aware of the limitations it entails, and that you are aware that you are no longer using a "FF" imaging system.
Exactly! And having invested a not insignificant amount for a FF MILC body, it seems a pity to cripple it by using APS-C lenses.
OK so my main lens is an EF 100-400. I asked the question to see if I could also continue using a couple of walk about EF-S lenses which would save carrying around my 7D. You've both answered my question and given me lots more to think about for which I thank you!
I suspect you will ultimately find which way you go depending on the specific shooting situation you're going for.
With any given EFS lens plus adapter, the mirrorless R6 will provide better autofocus, low-light sensitivity and higher frame rates, but at a reduced total image digital resolution of less than 8 Mp, whle the 7D will always give you almost 18 Mp to better utilize the len's intrinsic optical resolution. If you're shooting landscapes with a wide EFS lens that you're planning on printing at 16 X 20 the 7D would probably be the right choice, but for EFS tele wildlife shots or sports, the "cropped" R6 might be best.
As always, it's best to try your different possible combinations to find what fits your personal style. Above all have fun and don't get bogged down in the technical flotsum. Some of my most valued images were taken years ago using an Olympus C3040 with its 35-105 mm (eqv.) fixed zoom lens and only a 3.34 Mp sensor.