This is bad.
jpeg-xl offers very good compression and one special feature: It can transcode .JPEG in .JXL lossless, and saving 20% to 30% space. It simply takes the already existing JPEG compression data and transforms it directly into .JXL. Together with better compression, especially when using lossless, it shrank my picture collection about 50% since there were a lot of .PNG which sometimes can be compressed to 20% or their original size. While sill being lossless.
I even wrote my own .ps1.cmd (powershell wrapped in .cmd) to make it easy to mass-convert whole collection. Simply drand and drop a directory on it, and it goes on. Including a specific workaround since cjxl, the official tool, cannot handle unicode filenames. If there is interest I put it on my github.
Imagemagic and XnViewMP can convert too, though I don't know whether they use transcoding for .JPEG.