I'm working on writing a Shadowrun (sr5) mission that partly takes place in the Ork/Seattle Underground, and something I've been wondering is if there are any streets down there. My current understanding is that it mostly consists of narrow tunnels, but meanwhile I've not been able to find any source stating that there aren't any streets there. This thus leads me to wonder, are there — canonically — any streets where cars would fit (and realistically be suitable for someone to drive on) in the Ork/Seattle Underground in Seattle in Shadowrun sr5?
In areas controlled by prominent factions/gangs/law enforcement, absolutely.
The underground is described as containing a significant population of orks, trolls, and others in various conditions which aren't just tents in storm drains but also contains bases, armouries, tourist traps, malls, law enforcement offices, workspaces, workshops, corporate outlets and decent living accommodations (stretching to the even sybaritic).
This is a city of 200,000 people.
Now what you're thinking of - 'small cramped tunnels' - is a description of the seattle underground in the 1900s - it's 2083, omae. There's three main 'levels' of the underground, the dwarf controlled tourist trap (still got lots and lots of orks and trolls) which has KE and corporate presence, medic contracts, all the normal hustle and bustle of life. It's an absolute shoe-in that this has some areas where you can drive in, using car lifts to get to and from the surface (probably at a significant fee), as well as public transportation.
The Skraacha-controlled areas, which are generally described as more run down but still not like Redmond level bad, and which are usually 'lower' will likely have some areas that have public transportation or drivable roads and other places with narrower confines or throughways blocked by rubble/trash.
Then there's the uncontrolled areas which are very unlikely to be drivable, which are abandoned areas taken over by ghouls, spirits, cultists, you name it they've got it.
Remember, the key thing about the underground is that it's Big. Orks and other people have been digging and building down there for decades and decades, with all the singleminded focus of people with nowhere else to go.
However - you'll find official sources that contradict what I just told you. Thanks to catalyst's practice of hiring random freelancers and not doing any editing, SR5 (and 4, and 6) suffer from lore fragmentation - you'll find contradictions, sometimes wild ones, scattered through the various splatbooks and 'canon novels'. So in the end if you want the ork underground to be a warren of tiny, trash-filled tunnels that's really up to you as a GM - as long as you're consistent with your seattle, that's basically the best you're going to get out of current canon, which is generally very vague at the best of times and disagrees with itself on top of being frankly unbelievable at the worst.