I'm having trouble with a compound verb phrase (unsure if that's the correct terminology)

I would suggest that the comma is in the wrong place: moving it one word to the right makes it clearer that playing sports is an option for "a person" and that an athlete is a particular type of person.

I would add an extra verb because it's unnatural to 'return to ... sport' or to 'perform ... sport'. Sport may be pluralised or not, according to local style.

• This is so a person may return to performing everyday tasks or, for an athlete, playing sport(s).

I think it's alright that the athlete isn't described as a person here, because they're not an everyday person, which is clearly what you're implying.

Here's how I would change the sentence to be more parallel:

This is so a person may return to everyday tasks, or an athlete (may return) to (their) sport(s).

One problem I saw was that "person" was grammatically a subject, but "athlete" was the object of a preposition, which started causing the sentence to go down the wrong path. You also want the type of thing they are "returning to" to be the same, either a verb or a noun. I thought it would be easier to take out the verb, but you could probably add another verb that suits sports more naturally than "performing" to make the clauses more similar. I also thought, while not totally necessary, making "sport" plural emphasized that "sports" and "everyday tasks" play the same grammatical role in the sentence.

This is a little bit of a shoddy fix, so let me know if there are any major oversights in it.