Why is the PNG so much larger than the HEIC?

HEIC compresses far more aggressively. Converting to PNG keeps the full image but drops that compression, so a 3 MB photo can become a 20 MB file. That is expected, not a fault.

Does PNG keep transparency?

Yes, and it will keep it if your source has it. A photograph from a camera has no transparent areas, so the output is simply opaque.

Is PNG better than JPG for a photo?

Only if you are going to edit it further or the image must not change at all. For anything being published, JPG or WEBP will be a fraction of the size for no visible difference.

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