Every image format is a different trade-off between file size, quality and what it can represent — JPG has no transparency but compresses photos well, PNG is lossless and supports transparency but is larger, WebP mostly beats both at the cost of slightly less universal support. Converting between them means decoding the pixels fully, then re-encoding with the target format's own rules.
This runs entirely in the codecs already built into your browser, which is why the whole thing takes place on your device with no upload step and no server-side queue.
Your file is never uploaded, never queued on a server, and never deleted from one — because it was never there.