Does PNG restore lost JPG quality?

No. Detail a JPG threw away is gone. PNG only stops any further loss from here on.

Will the background become transparent?

No. JPG has no transparency, so the PNG keeps the same solid pixels, including any white background.

PNG stores every pixel exactly, and photos have a lot of fine detail. It's normal for the file to grow several times over.

No. Converting happens in your browser with WebAssembly, so nothing is sent to a server.

JPG to PNG

Save a JPG as PNG so further edits don't lose any more detail.

Runs on your device. Nothing is uploaded.