No they’re equally correct.
https://forum.wordreference.com/threads/fr-sinscrire-dans-à....
Re:I Learned French in 12 Months
by mytailorisrich on Sunday February 16, 2020 @03:38PM
(#22343606)
Both forms are equally correct in some cases but not all cases.
In this case, 'dans' is at the very least 'more correct' than 'à'.
In fact, the only correct correction among all that red is to replace "gym" by "salle de sport". Not to be confused with "gymnasium", it's similar but not the same thing.
The 4th line is misusing the future tense. Should have been pointed out.