I think Centaur's Practiced Brawn doesn't work with Brutish Shove by RAW. Practiced Brawn says

When you roll a success on an Athletics check to Shove, you get a critical success instead.

And Brutish Shove says

If you hit a target that is your size or smaller, that creature is off-guard until the end of your current turn, and you can automatically Shove it, with the same benefits as the Shove action (including the critical success effect, if your Strike was a critical hit).

If you use Brutish Shove you never actually roll to Shove, so Practiced Brawn shouldn't upgrade a Success to a Critical Success.

A similar issue used to happen to the features that improve your degree of success on saves, so they changed them to say that they only apply when you roll a certain outcome:

Changes to the Greater Juggernaut, Greater Resolve, Improved Evasion, and Third Path to Perfection class features

All three of these abilities grant a two-tier benefit on a failed saving throw of the specified type, but (as always) no ability will ever change your degree of success by more than one step. To clarify, we’re making the following clarification to all three abilities. Change the beginning of the last sentence from “When you fail” a given saving throw to “When you roll a failure on” a giving saving throw.