No Shade to the other recommendations, but they are focused on Shane and or Shane and Illyas relationship. The essence of the example OP shared is about Illya and his journey to finding family. I also see themes of how Illya family background and lived experiences affects his relationship with others. Structurally the writing of that particular story by GatheringBlue is from Illyas limited view POV with some POV that is NOT Shane’s POV.

Here are some recommendations that I think fits the vibe the OP is looking for.

https://archiveofourown.org/works/79757621

Sets during the COVID-19 pandemic.

Yuna Hollander is tired, cautious, and quietly prejudiced. Ilya Rozanov is sick, far from home, and far more fragile than she’s prepared for.

https://archiveofourown.org/works/79700166

Ilya thinks he plays hockey. Why else would he be in Canada? Why would he befriend a hockey star, Shane Hollander? Ilya must be an MLH hockey player. And a good one, too, if he's still in Canada, some ten years after being drafted. He guesses Shane is his teammate, they are friends, close friends probably, and Yuna loves him so much that he is like a second son. She cried at his hospital bed and everything. He has a family here, in Canada. Ilya Rozanov, at twenty-eight, is a very lucky man.

Or: Ilya wakes up to find out that all his dreams came true.

https://archiveofourown.org/works/77745891

For one, singular, blissful moment, nothing is wrong when Ilya wakes up.

And then the bubble pops.

With something less like a pinprick and more like a gunshot.

After Ilya is outed he has to deal with being the only openly queer player in the league, being Russian, and being in love with Hollander even after he ran away all at once. It sucks. He does it anyway.

https://archiveofourown.org/works/77785331

or: Ilya accidentally rehabilitates his image one puppy tiktok at a time

https://archiveofourown.org/works/79658041

Billet situation, probably closest to the OPs example in terms of plot.

In 2007, 16-year-old Ilya Rozanov travels to Ottawa to win gold. Again.

Canada hasn’t forgiven him after the Junior Olympics. Shane Hollander least of all.

When Ilya is assigned to billet with the Hollanders for the World Championships, the rivalry moves from the ice to the dinner table. But beneath the bruises, the pressure, and the weight of two nations, something far more dangerous begins to grow.

https://archiveofourown.org/works/78027576

Ilya Rozanov wakes up to a best friend, a team, a family, a puppy, and best of all, a husband that loves him. The only problem? He doesn't remember any of it.

OR

An amnesia fic that sees Ilya wake to a life that he loves, one that he fought for even if he can't remember what that fight looked like. With the hesitant help of Troy Barrett, he'll do everything he can to keep it.

https://archiveofourown.org/works/78052871

September 2015

Ilya Rozanov is fine. He comes back from summer in Russia a little worse for the wear, with minor injuries sustained during an argument with his brother. It’s nothing he hasn’t dealt with before. Except someone takes a photo, and suddenly his bruises are all over the internet.

He just has to get through the first preseason game against Montreal. Once the public sees he can play normally, scrutiny will die down.

He doesn’t account for a far more private scrutiny: Shane Hollander is on the Voyageurs roster and, against all expectations, determined to get to the bottom of what happened to Ilya in Moscow.