Can a JPG have a transparent background?
No. JPG has no alpha channel, so a "transparent JPG" is always flattened onto a colour, usually white. For transparency, save as PNG or WebP. If a form or marketplace insists on JPG, add a solid white background in the editor and export the JPG from that.
This is why a logo that "was transparent" arrives with a white box after being sent as JPG: the transparency was discarded on save. The fix is to go back to the PNG source — or re-run the JPG through bgclear, which produces a transparent PNG from it.
PNG is lossless and universally supported; WebP is much smaller and supported by every modern browser and most apps, but not by every older tool. When in doubt, PNG.