Space is only -1 atmosphere and even then, it only affects sealed systems. For the rest, they'd equalise. Also, cooling in in space is actually fairly gradual as there's only radiation, not convection or conduction. Let's go through the systems and evaluate what that means:
For structural components, nothing will really change. After all, we built spacecraft out of aluminium before. The ISS has to cope with this more, as it goes in and out of sunlight every 90 mins, so it gets something like 15 cycles of high/low temperature a day. The thermal shock of going from darkness to sunlight is the main issue, but this won't be passing through the earth's shadow constantly since it'll be orbiting the sun, so changes will be far more gradual.
Bigger issues come from different materials joined together, such as steel to aluminium, since they expand at different rates, but that's not really a problem here and even if it is, it'll just crack a bit at the seam. That's not going to cause the car to explode into little fragments.
For unsealed systems with fluids, they'd just boil away in the vacuum before desubliminating into little frozen droplets and bounce around or whatnot.
The only sealed systems with fluids in them that I can think of are tyres and brake lines. Tyres tend to sit at about 30-35 PSI, which is ~2 atmospheres. They then have to endure significant heating/cooling, dynamic pressures of spinning, etc. so an extra atmosphere wouldn't cause issue from a pressure point of view. Ditto brake lines - you stomp on them with a mechanical advantage and they never rupture.
I think you'll find the worst damage will be to the paint over time, which will fade more aggressively since it's not protected from UV sunlight any more.
edit: I forgot the batteries, which I believe are a sealed unit. They might have just dropped the battery pack from the car. Not sure what a vacuum would do to them as I don't know enough about Li-Ion battery design to comment.
"We didn't really test any of those materials [...] it's just literally a normal car in space"
After all, where it's going it won't need roads.
The glass will eventually become clouded and discoloured due to radiation damage and scoring by micrometeorites. Some plastics can rapidly deteriorate in sunlight.
Erosion from micrometeoroids (dust) and larger impacts is also a factor over timescales of thousands of years.
I doubt it will last the millions of years that is suggested.
id imagine a 360-camera is projected onto the inside of the sphere/case the car is actually inside of.
Like, remove any fluids, remove any parts that might explode in the hot or cold of space, deflate the tires, etc.
Note: I'm more interested in a scientific answer, as opposed to casual conjectures. Preferably from an engineer knowledgeable of such things. And specifically, the materials sciences aspect of how materials will survive in a vacuum.