Jpeg XL is based on PIK and FIUF, where FIUF is the successor of FLIF. Jpeg XL will contain the technologies developed in FLIF and later in FIUF - the efficient progressive mode is from FLIF.
The problem with FLIF and why the author later created FUIF is that FLIF doesn't have a lossy mode (well it was lossy if you just downloaded part of the data but it was very inefficient). A nice thing of FUIF is that it can losslessly transform a JPEG file into a FUIF file (well it uses just a subset of features) which is smaller than the original (because of better entropy coding).
PIK (from Google) is also interesting as its main goal is to be more efficient than JPEG but with not much bigger complexity, so it has a lot of goodies invented since JPEG was released to increase the quality but not complexity. It's not as efficient as HEIF or AVIF however.
I'm looking forward to try it out - I think it has the potential to replace JPEG, at least in some segments, but that doesn't really depend on the format itself.