Das Einzige, das zählt, ist dein Glück.

English Translation

The only thing that matters is your happiness.

Any way to tell that this sentence isn’t referring to ‘your luck’?

No, without context, it’s impossible to know whether “luck” or “happiness” is meant.

A more natural phrasing would be:

“Das Einzige, das zählt, ist, dass du glücklich bist.”

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English Translation

The only thing that matters is your happiness.

The translation is stil wrong, “The only thing, that counts”, das zählt = “that counts”

It’s not wrong. It’s just not the closest possible translation (but still close enough).

You could also say:

“Das Einzige, das etwas bedeutet, ist, dass du glücklich bist.”

You could say many things, but it didn’t. When people are trying to learn a langauge they need to be able to learn the proper meanings of words, not the many ways it could be translated, at least not until they have it down. These kinds of loose translations are murder for learners under C1