My sim is level 6 in the military and has had max performance for several days with no promotion.
I do have the story progression settings set to allow some career levels to "restrict some levels to a single sim(true)" but also "only one may lead: allow active (true)".
My sim recently moved from another town, and her previous boss still shows up in her relationship panel. I really don't know what the issue could be though.

What you are describing is what is supposed to happen if another sim in town is already at Level 7. Your sim must have participated in the Only One May Lead scenario and lost out. If you want the actively played sim to always win on those scenarios rather than compete, then the Allow Active setting should be False. Or you can wait for the other sim in town at that level to be promoted or demoted out of it (or move away, retire, change careers, die...).

Note though that if you switch active households, your sim may sometime in the future get demoted if another sim comes along and competes for that level again.

I'm not sure that's it. For one, all the other coworkers are like, latrine cleaners.
but also because I just realized she hasn't aged since coming to town. I think she may actually be younger, but that seems impossible.

Does your sim have Level 9 Athletic skill and Level 8 in Handiness? These are required to get promoted to Level 7 in the career.

And you are certain there isn't another sim in town who is Level 7 in this career already? Not among the co-workers that appear on the relationship panel, those might only be a subset of all sims in that career.

If none of that pans out you may need to use MC to specify a different boss for your sim, as they wouldn't really be expected to maintain a good enough relationship with one who doesn't live in this world.

NRaas > MC > (Sim) > Intermediate > Career > Choose Boss
(MC Cheats module required; note that technically the boss doesn't need to be at a higher job level than the subordinate)

Yeah she'd maxed all her stats by the time she finished college Too easy.
When I use MC to check on sims in town, it says she has 9 coworkers, 3 level 1, 4 level 2, 1 level 4, and then 1 level 6 (her). There's one sim in her relationship panel from a previous town who i cannot see what career level she is, only that she's military. And her boss from out of town. But she has an in town boss, and is good friends with him, and it shows up that her boss career performance is green.
but I'll still try switching her boss and see what happens.
Formerly I'd had the promote immediately setting set to true, and it was working fine. I turned it off to see if it would fix something.
I'm about to send her on vacation. Also I think I'll use traveler to fix homeworld? Maybe there's a problem from when she moved here.

Fix Homeworld is a DebugEnabler command, not Traveler. But yes, that is a good idea.

Well, I tried everything.
none of the other sims in town were at the level she was.
I changed her boss.
i turned off the settings that would keep only one sim in certain jobs.
finally I just had to manually promote her. I'm going to see if somehow that fixes it, but if not, I still don't know why she can't get promoted.

Ah, I thunk I figured it out. I forgot I had job overhaul. I googled and some other simmers reported issues with getting promotions as well. It makes sense since I think there's supposed to be some kind of promotion interview, but I bet it's messed up for some reason. I wish I'd remembered that sooner. I don't use many mods, mostly only nraas mods, so I assumed I'd borked the settings and reset them.