Many sporting events and venues that issue media passes to professional photographers do not permit or restrict the size and/or type of cameras that regular paying customers sitting in the stands are allowed to use.
Please research this for any event or venue that you plan to attend with a camera in your hands. You might be limited to lenses that are up to 4 inches, or 10 centimeters, in length, which assumes that you can even bring a camera that uses interchangeable lenses.
Capturing photos at a distance from your subject is challenging. The farther away you are, then the more diffraction effects you will encounter from the intervening air. An extreme example of what I am talking about would the visible heat waves you can see rising from hot street pavement.
The purpose of a super telephoto lens, >300mm, is to enlarge your subject in the viewfinder, not capture images from great distances as if you were using a telescope. Keep that in mind if some of your images seem a little soft. Getting as close as possible to your subject is the key to sharp images.
What lens would I recommend? At your budget, I would not recommend any lens. If you want a quality super telephoto lens, then it will cost at least 2-3 times your stated budget of 700€.
Are there lenses out there within that budget? Yes, there are new and used lenses out there. Most of them are all EF mount, third party lenses. There is no guarantee that a third party EF mount lens will be fully compatible with all the advanced focusing and tracking features found in Canon R Series of cameras. You should expect AF performance to be degraded in some way, especially if you shoot video.
Most third party EF mount lenses cannot keep up with the high frame rates. That means the gear does not refocus fast enough to keep up, which usually means the lenses do not refocus fast enough to keep up with the advanced subject tracking features.
The lack of full compatibility with the AF system is also true for many of Canon’s older EF mount lenses. Here is a page that can be found in both the R5 and R6 User manuals.
