Careful with the JPEG-XL re-compression, though--depending on how you're re-encoding, jxl may use SSIM to evaluate for visual losslessness, and the whole point of TFA is that SSIM is blind to posterization, but (some) humans aren't.
Disk space is cheap. It's most likely not worth the 20% compression to lose your original images (and possibly lose metadata as well--it's quite hard to robustly retain all vendor-specific MakerNotes, for example).
JXL has Guetzli lossless JPEG compressor integrated into the standard so it produces reversible and completely standard compliant JXL images that are 15-20% smaller size.
Reversible in sense that you can still convert the image back the original JPEG, that is bit exact file as the input JPEG was (it takes care of all the metadata also - it has to).
Also if you decide to forgo the reversibility you can get a bit more out of it as JXL is actually a superset of JPEG, so it can read the JPEG stream and convert it to JXL without complete recompression - it will just use more efficient structure of JXL and much more efficient (ANS vs. Huffman) entropy encoding. The additional savings compared to the reversible mode aren't big however.
My impression is that this is more or less how ISO standards are supposed to work. Personally, I don't want to work in such an environment.
The process has its issues and could cause problems, but in practice I don't remember anyone reporting issues.