"he's a perfect fit for you" or "he's the perfect fit for you"?

It will depend on the context. I'd say "he's the perfect fit" for something like a soulmate, where there's one perfect person for you. If I was looking for a house to buy and found a good one, I'd say "it's a perfect fit," since there are probably multiple perfect houses for me, and this is one of them.

It should be 'the' because it implies that he is the only one. But you could say something like 'it's a perfect fit for you' if you were referring to maybe some clothing because there will be many pieces of clothing that suit you perfectly

it should be "the perfect fit"

For objects, it's a perfect fit. So when I find a slice of pizza fits into a lunchbox, I could say 'it's a perfect fit' For romance, he's the perfect fit. The because there's not multiple things that can be perfect, just one.

If it’s a test/classwork scenario I’d go with “the” since perfect is theoretically impossible to achieve. Additionally, he is the perfect fit, key being HE; there’s only one of him.

“The perfect fit” would work better because it’s definitive. “A perfect fit” implies maybe there’s another. “Can you pass me A pen?” (Doesn’t matter which one just a pen) “Can you pass me THE pen?” (Maybe the one right in front of you or in your hand rather than the one elsewhere in the room).

A perfect fit is ok because this phrase is a metaphor. It is being used figuratively - clothes fit, not people. The original meaning of the noun is about clothing.

A perfect fit. It's an idiom

Then it depends on what you believe about whether there's only one or several, doesn't it? You can express either.

You could use both, but "the perfect fit" is much more standard without context.

Either is fine. And yes, it comes down to subtle nuance. Is there only one perfect person? Or are there many possible perfect people? That's a worldview question, not a language learning question. Also context matters - talking about what a great relationship someone has with their spouse, it's more polite to call them "the perfect fit". Talking about the guy your friend met last week and are going on a first date with, maybe they are "a perfect fit" because of their unexpected shared interests in tap dancing and speed knitting.