The App Store forbids any app that violates the terms of service of any company [1], regardless of the legality [2]. Since YouTube forbids alternative clients in their terms of service, Apple will not allow Grayjay onto the App Store. Even in the EU, where multiple app stores are available, you still need to follow a subset of the App Store guidelines. I looked through them and it appears that the ToS violation guideline is in fact exempt for EU apps [1], so they could release a version in the EU exclusively. However, they may be subject to the Core Technology Fee.

[1] 5.2.2, 5.2.3: https://developer.apple.com/app-store/review/guidelines/#int...

[2] https://www.eff.org/deeplinks/2020/04/federal-judge-rules-it...