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)