"Sunk into depression" isn't insanity yet. It is part of the way to insanity.
Insanity would be "stricken by melancholy" for someone who falls into depression one too many times.
"Haggard" (at least not "Harrowed" yet) is another part of the "journey" to insanity. It goes from "Stressed" (yellow) to "Haggard" (red) to "Harrowed" (purple). Dwarves (and other test subjects intelligent, stress-susceptible creatures) in those stages will "stumble around obvliviously", throw tantrums or "sink into depression". Watch out for those stressed dwarves, I had my absolutly willing test subjects stressed goblins and troglodytes destroy a retractable bridge and restraints under them on multiple occasions, and I strongly believe that dwarves MIGHT do the same. The circumstances how that happened are still unclear to me though, I think it might have to do with "throwing items around during a tantrum".
Anyway, going off course...
I find it quite weird that she is "Haggard" at only 30k stress. All tests I did had the subject only go haggard at 250k+. I had one subject turn insane before going harrowed though! You will notice when that happens, and the subject will eventually die (unless it doesn't need to sleep, eat, drink and is prevented from jumping off high places etc. - but it'd be a bit pointless and impossible without moding to keep an insane dwarf alive unless it might otherwise cause the whole fortress to go insane).
She should still be able to get better over time if you give her a nice room, good meals, alcohol...all the happy fun stuff. And lots of it.
I'd guess though, as you said the stress doesn't go down, that she is both highly susceptible to stress AND doesn't feel the slightest bit cheerful about anything and/or got other traits that make stress reduction difficult.
I had a few of the "never-happy"-dwarves in my fortresses, but luckily never a combination. They are hard to keep happy, it is always advisable to disable refuse hauling on dwarves like that.
Though I also had one of my carpenters increasing stress without it dropping much from all my great stuff I have around him - and he doesn't show any personality traits that explained why he'd end up with way more stress than any other dwarf. I turned off the refuse hauling which subsequently kept him away from seeing the bad stuff and which caused his stress to go down over time. (He didn't get to "stressed" though, I keep a close eye on my dwarves and thanks to all the high quality things I got around them - including proper rooms and platinum statues as well as artifacts and all - almost all are at -99999.)
If she is a real problem, there are of course lots of fun things one can do with annoying dwarves, be it velocity tests in a garbage dump shaft or finally getting that magma supply tunnel open which you misplanned somehow. Just remember to give her a grave/engrave a slab.