Why doesn't game pass ultimate work with Skate 3?

Skate 3 is an EA title, and therefore will likely remain in EA Access. There is a free trial, and a free month with Game Pass Ultimate,

Skate 3 is purchasable. It's $3.99 USD in the store right now. You may be seeing it as free because it is part of EA Play which is included in Game Pass Ultimate. So if you cancel the subscription, you will lose access to that game as well unless you purchase it.

Hello, this is Manuela. I'm an Independent Advisor and community user like you, ready to assist with this.
Not a Microsoft employee.

I’m sorry to hear you’re having some trouble when you try to use the game pass discount to purchase eligible games. Let’s try to sort this out.

However, before that, I would like to ask the following questions:

Did you purchase the subscription today, or when?
May I know if you tried to purchase the desired game, or games, using the Xbox.com website instead?
Is the subscription active on your account?
https://account.microsoft.com/services

This is a great question, thank you for posting it!

Skate 3 is an amazing game! I haven't played in a while, but every time I'm in a GameStop I will see a copy. That is a type of game I would love to see come to game pass. I've had my Xbox game pass ultimate subscription for about 8 months now, and it is
the best deal in gaming!

check here https://account.microsoft.com/services/ to see if you have Game Pass Ultimate or just Game Pass.

if it is just Game Pass for Xbox then see if you can find the deal for 3 months of Ultimate and get that and it will upgrade your existing Game Pass to Ultimate as well as adding the 3 months of Ultimate (you should end up with 5 months of Ultimate for a
total cost of 2 Euros which is a sweet bargain)

if it the link I posted confirms that you have Ultimate then you will need to contact Support to find out why it won't work with your PC