Simply opening a JPEG does not reduce its quality. JPEG quality loss happens when the image is edited and re-saved as JPEG, not when it is just viewed.

So if your only concern is quality loss from opening the files, you do not need to convert them. Converting existing JPEGs to PNG or TIFF now will not restore any detail already lost to JPEG compression, and it will not improve image quality. It will only preserve the JPEG’s current state in a larger lossless file.

For archiving, keep the original JPEGs unchanged. If you want to edit them, make your edits and save the final result in a lossless format or keep separate edited copies so you don’t repeatedly recompress the same JPEG.

If you also have the original camera RAW files, those are the best long-term source to keep alongside JPEGs. But if JPEGs are all you have, keeping the originals untouched is the key point.