Currently written, your sentence has two distinct differences from passive voice:
- You can't add the agent into the sentence with by:
WRONG: The car finally broke by me
- There is no "form of the auxiliary verb be"
(These two distinctions are closely related—adding a form of be will allow you to add by: "The car was finally broken by me".)
Your other choice is (usually)... active voice. Yes, as far as most are concerned, there are only two voices. APA would be a prominent example. But you already ruled out active voice for the obvious fact that the car isn't breaking anything—it is the one that is broken, the "object" of the action.
It's really only linguistics that uses the other categories you mentioned, usually for reasons exactly like this (for English at least). You did get those terms off this Linguistics answer, right!? However, there is a lot of variance with how each term is defined from paper to paper, as this answer indicates. "Middle voice" is just one of the many terms used to describe this use of "broke", according to Wikipedia:
Patientive (S = O) ambitransitives are those where the single argument of the intransitive (S) corresponds to the object (O) of the transitive. For example, in the sentence John (S) tripped and John (A) tripped Mary (O), John is not the person doing the falling in both sentences. Likely candidates for this type of ambitransitive are verbs that affect an agent spontaneously, or those that can be engineered by an agent. English has bend, break, burn, burst, change, cool, enter, extend, fall, frighten, grow, hurry, melt, move, open, spill, stretch, trip, turn, twist, walk, and many other verbs.
Verbs of this class have been called unaccusative verbs, middle voice, ergative or anticausative verbs in the literature, but again, these terms are not universally defined.