Not sure imagemagick supports lossless transcoding. This old discussion from 2021 mentions that it didn't (in 2021):

https://github.com/dlemstra/Magick.NET/discussions/872

cjxl / djxl do lossless transcode reliably when called with all defaults (no arguments). Just re-checked:

  $ cjxl src.jpg out.jxl
  (some output)

  $ djxl out.jxl rev.jpg
  (more output)

  $ cmp src.jpg rev.jpg 
  (no output: files identical)

JPEG to JXL transcoding and JXL to JPEG reconstruction are different from converting an image in either direction, it's gonna be a specific option (in something like xl-converter), so maybe it wasn't what was used and it was just a "reencode" into jxl and then into jpeg.

It probably used pixel-by-pixel conversion (decode input format -> encode output format), which is lossy, not the libjxl native way to convert JPEG (it needs to know about the original JPEG data, not the raw image data).

Image Magick re-encodes into an internal format, before output. If reproducibility is the goal, I'm afraid it just isn't the right tool.

(The IR used to be PixelPacket. Not sure how modern versions handle it.)