Sounds like a lot of stuff piling up. One part of good boundaries is to understand what is your issue, and what is your bf's issue. That reduces your stress a lot either way: If it is YOUR issue, you can solve it yourself. If it is his issue, you don't need to solve it at all.
Of course, he has horrible boundaries and mental illness... .so he will insist that his issues are yours, etc... .making it that much more confusing to sort it all out.
I have a hoarding issue.

You know that one is yours.
I haven't made decluttering and cleaning my car a priority. It's pretty terrible and the floorboards look bad.
Yup, this one is yours too, and you know it as well.
I told my boyfriend I dont want to be the designated driver for that reason. He still demanded I do it.
His demand that you drive him around is on him, not on you. OTOH, you cannot force him to drive you anyplace. You also don't have to let him in your car.
And then the complaining starts.
Consider telling him that there is a new rule: "Passengers in your car will shut up about the mess in there." And if he doesn't, pull over, and ask him to get out of the car. Or drive back home and drop him off. Or at least pull over and inform him that you aren't driving anywhere while he's complaining about your car. (i.e. if he cannot shut up about the mess, he cannot ride in your car.)
Enforcing that rule would stop those complaints 100%--at least while you are in the car.
He wants to pay 150$ to get my car professionally cleaned.
He gave me an ultimatum that either I get it cleaned out by this week or he'll pay for it to get cleaned.
I'm assuming that the two of you have (mostly) separate finances. In that case, he can choose how to spend his money... .and if he wants to be generous and offer to spend money on getting your car cleaned, he can do that. HOWEVER, it is your car, so you aren't obligated to let him do so unless you want it done yourself.
I don't want his help because he's being horrendously judgmental and critical of me.
Yeah, the emotional baggage attached to that threat/offer on his part really takes away from it. He's doing it to manipulate you, not to be generous.
Imagine a good friend saying: "You seem really stressed out by the mess in your car. Can I help in any way, perhaps paying to have it cleaned?" It would feel very different.
I'm not suggesting that your bf is likely to take this approach, especially considering where he started... .but you can take the offer quite literally and let him do it anyways... .and refusing to pick up the guilt and crap he's throwing at you with it.