I am assuming you have field access so you will be close to the action and can move around to follow it, if so then the 70-200 f4 is workable at night with GOOD field lighting but if you can figure out how to stretch your budget then the 70-200 f2.8 is something you will not regret as a long term purchase and is far better for night games.
If you are further away from the field, then a 200mm max telephoto is going to be somewhat limiting. I don't believe Canon's 1.4X converter is compatible with the RF version of the 70-200 lens so that takes away a fairly easy method to extend the lens.
So if you don't have close access, let us know because the lens answer is going to be different!
I use two full frame bodies (1DX III) with a 70-200 f2.8 on one and a 400 f2.8 on the other for soccer. The only exception is for day games I will sometimes use a 200-400 f4 with integrated extender instead of the 400 fast prime which allows me to capture offensive action moving towards one goal by being near that goal while still capturing saves at the far goal. During night games, I shoot with the 2.8 glass wide open, in the day I will generally step it down to f3.5 to f4 for a little more depth of field unless it is a field where I definitely want the shallowest DoF possible.
On Edit! The forum software reordered the images after I posted so go by the captions on the photos for the lenses involved. Two are with a 70-200 f2.8 lens, another two with a 400 f2.8, and six are with the 200-400 f4 extender, and three of those with the extender engaged making it a 280-560 f5.6 lens. I have never had the forum software put photos differently than the order of entry so lesson learned!
You will be moving around a lot to do good coverage with a 70-200 lens, especially at night where ISO is pushed higher and extreme cropping is going to be less desirable and that is exacerbated if using the f4 version which will double the required ISO for a standard exposure unless you drop shutter speed which isn't desirable.
Rodger
