I think your understanding is incorrect. Converting a JPEG to PNG doesn't magically aid in quality preservation as you edit an image. Essentially, when an image is opened in an editor, the filetype that the image had been stored as is irrelevant; you are simply dealing with pixels that each have a RGB value. (These are 8-bit values in the case of JPEG.) When you push these pixel values around (i.e. applying edits to the image), new RGB values are calculated for the pixels. It doesn't matter if the image was a camera-original JPEG file or a PNG file saved from that original, the RGB values are going to be the same.

The difference comes when the image is re-saved as JPEG. It's at that moment that lossy compression is applied for JPEG files, and that's where quality is theoretically lost. If you were to save as PNG or TIFF, no lossy compression is applied. (Personally I prefer TIFF – probably things have changed, but there was a time when PNG didn't support colour profiles.) Re-opening these 2 hypothetical JPEG / PNG files can result in different RGB values for some pixels. This loss in quality however, based on re-saving a high-quality JPEG file as a high-quality JPEG file, one time, is negligible. You won't notice it. Still, if you intend to apply further edits, it makes sense to save your file using an image format that doesn't apply lossy compression.

The big difference is between 8-bit and 16-bit files. When you push pixel values around in a 16-bit file (i.e. applying edits to the image), then new RGB values are calculated with more precision, and there's more "room" for gradation between colour values. Especially for editing, 16-bit images are more, let's say, "desirable" than 8-bit images.

This explanation is a simplification, but hopefully adds something.