I always thought that Legolas would leave Arda before Thranduil and the rest of his people because of the sea longing.
The only reason he even stayed to begin with was becssue of how much he loved Aragorn and Gimli. If it weren’t for them i feel like he would never have stayed so long. And so, right after Aragorn dies and it’s decided Gimli will come with him, Legolas makes one last trip to his forest before he departs the shores forever.
And so when he gets to Valinor he’s alone, aside from Gimli.
Nobody in his family had been released from the halls yet, and Thranduil (his only blood relative left) is an ocean away. So he finds where Elrond and Celebrian are staying and shows up on the middle of the night with absolutely no warning.
Elrond and Celebrian had already decided he was going to live with them until Thranduil arrived before he even said a word.
He may not have any blood relatives around, but there was an entire family already waiting for him.