No Easy Answers
Even restricting to science fiction and fantasy genres, you could write volumes on the role of coincidence in good or bad narratives. And then you'd have to disregard a lot of that work because RPGs are not narratives in the same sense as novels or movies.
Not to mention, there is a fundamental matter of taste and style from player to player.
Therefore, I tend to treat coincidence as a scarce resource, which renews itself slowly if at all. And here's the kicker: I, as a GM, never know how close to the edge I'm dancing, because the ultimate authority is the audience, your players.
What Is The Purpose Of The Coincidence?
That said, I try to answer that question-- what is the purpose?-- to try to evaluate whether the coincidence is worth spending, so to speak. Player/character agency is central to modern gaming, so that is the lens I try to use.
Is this a coincidence that will set one or more players up for an interesting choice? A revealing choice? A choice that will define their characters or have manifest impact on the game as it goes forward? If yes, then it's probably a good coincidence, a coincidence that leads to agency.
Is this a coincidence that just gets the characters to do what I want them to do, or be where I want them to be? If yes, then it's probably a bad coincidence, because it is restricting their agency.
These are not absolute, of course: Sometimes, players use their agency to do something really catastrophically dumb and a quick coincidence saves the game. (After all, it's hard for anyone to have agency if Sauron wins.)
And even for those good coincidences, there is a built in tension: If you are throwing so many coincidences at the players that they see one every other session, that starts to feel like a systemic reduction in agency because they're probably not reaping the full rewards (narratively, anyway-- sometimes a narrative reward means hard luck for the character) of the choices they made a session or two ago.
So Ask Yourself This:
What is the point of having them run into this wyrmling again? (And indeed, a more philosophical question is: What is the point of even having character backgrounds?)
Is it to illuminate something about the characters? To cause them to reveal something about themselves? To force a difficult choice? If it isn't... can you tweak the idea until it is?