Yeah they generally have statsus effects, thats what they have now. i dont know about vampire and catmancer, not sure if those would be considered blue mages, but all the rest have things like doom level 5 petrify, gravity type attacks, a few elemental etc. Also blu mage has some physcal enemy skills.
looking at the blu magic page, looks like ffxiv version aligns very closely with the vast majority of iterations of blue magic and blue mage in its implementation. The most common factor is learning skills from enemies, and conditional spells like white wind, mighty guard, doom, missle, bad breath, 1000 needles, self destruct etc.
kimahri has access to these type of spells, as well. only the non blue mages from non ff games seem to be that different
https://finalfantasy.fandom.com/wiki/Blue_Magic