JPEG is lossy. Every save throws away more coefficients. If the next tool will edit the picture — crop, overlay type, save again — converting to PNG first means those edits are lossless from that point on.
PNG will not bring back eyelashes or brick texture JPEG already smeared. If the JPEG looks soft, the PNG will look the same, just heavier.
When not to bother
If you are posting a photo to the web and you already have a decent JPEG, stay on JPEG or convert to WebP (webptools.com). A PNG of a photo is often two to five times larger with no visible gain.
Transparency
A JPEG has no alpha. The PNG you download is opaque. For graphics with holes, start from PNG or WebP, not JPEG.