How does "I happen" work in this sentence?

"I happen to find one after I've met you."
"I happen to be the parent of the owner of this restaurant."

I've found this kind of sentence in the RPG game I'm playing last and I don't think this sentence was wrong. Can you explain how does it work in the sentence and at the first glance, the sentence looks very wrong for me.

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To happen, in colloquial speech has a couple meanings.

Usually, it just makes speech sound more polite.

Ie. I happen to find butterflies beautiful.

In this case, it's contrary to someone else's opinion.

In your example, it means "by chance" or coincidentally" or just "in relation to what you're talking about" or just make an assertion about something.

"I happen to find one after I've met you."
This could be in response to someone talking about looking for something, and you want to point out that you already found it by chance, or coincidentally, or unexpectedly at that point (after I've met you).

"I happen to be the parent of the owner of this restaurant."
This could be in response someone talking about the restaurant and you want to point out that you're the owner.