I had a T3i and it served its purpose, but you're correct that it's time for an upgrade.
Why use manual? And I say that as a working photographer for 45 years. If I'm trying to do action shots, the last thing I'd want to do is fiddle with setting the exposure. If anything, I'd go with shutter priority mode.
I used my T3i as one of my cameras up to a year and a half ago when it became so outmoded that I gave up using it as my everyday/basic/go-everywhere camera body.
I replaced it with the ultra-cheap--but ultra value R100--and I have shot heavily with it. It's a good camera, but I also have an R8 that is a tremendous camera.
For sports photography, the T3i will bump up against it's 6400 ISO though you can squeeze out 12800, but I found that noise explodes after 800. If you couple that with a lens that does not have a fast aperture, you're in a bad way for sports photography with a T3i.
Option 1: go with a cheap solution via an R100 body and an EF-to-RF adapter and you could use your lens on the new body that will go to ISO 12800 without the lousy noise of a T3i. You'll still have noise, but not as horrific as the T3i. Noise is in action photography is kind of a given.
Option 2: get an R100 for cheap and spend big on a fast lens. The lens would be where I'd put my money if I had to choose between a higher-end lens versus a higher-end camera body.
The R100 is not the best choice for a body, but it would get you either a much better camera for your current lens for cheap if a faster aperture lens is not in the cards or not break the bank on body price as you level up on a fast lens.
Option 3: go with an R8 that can reach ISO 120,400 natively and adapt your lens with an ER to RF adaptor. The R8 has an accessible price point.
Option 4: R8 + fast lens.
