PNG cannot recover what JPEG threw away
JPEG compression is lossy and permanent. When the file was created, detail was discarded - fine texture, sharp edges, subtle gradients - and the artefacts around high-contrast boundaries were baked into the pixels that remain. Converting to a lossless format preserves those pixels perfectly, artefacts included. It does not reconstruct anything, because the information to reconstruct it from no longer exists in the file.
So a JPEG converted to PNG is a larger file containing exactly the same picture. If someone has asked you for a higher quality version, the answer is the original source file, not a conversion of the compressed one. This is the single most common misunderstanding about image formats and it costs people a lot of disk space.
Nor does it create transparency
PNG supports an alpha channel; JPEG does not. That means a JPEG has no transparency information to carry across, so the converted PNG has a fully opaque background of whatever colour was in the photograph - usually white, which looks transparent against a white page and stops looking transparent the moment it is placed on anything else.
Removing a background is a separate operation entirely: something has to decide which pixels are subject and which are backdrop, and that is image editing rather than format conversion. Convert first if you need PNG for another reason, then remove the background in a tool built for it.
When converting to PNG is the right call
There are good reasons. A system that only accepts PNG uploads. A design tool or print workflow that wants lossless input. An image you are about to edit repeatedly, where each re-save as JPEG would compound the compression - converting once to PNG stops that generation loss even though it cannot undo what already happened.
Screenshots, diagrams, logos and anything with text or flat colour genuinely belong in PNG, and if one of those reached you as a JPEG then converting is a repair rather than a waste - the file will be larger, and it will stop getting worse every time it is edited and saved.