Can Apple AirTag give us a registered tracked route?

If the AirTag places the car in that location, then its likely correct. They will claim its garbage, but in general AirTag tracking relies on other Apple devices to triangulate the AirTag's location, so its highly unlikely multiple devices (iPhones, iPads, and Macs) reporting an AirTag nearby would provide a inaccurate location for it.

As such, AirTags are fairly accurate. You can sue the parking garage for misuse of the car and use the AirTag location as possible evidence. Best you consult a lawyer though.

Sometimes, in an area where service is not very good, the AirTag (or a phone, or a Tile, or an Android phone, etc...) can show that it is in an area that the device may not really be in, but would show a circle that the device could be in. 5Km is a lot further than I would expect that range to be. But inside a car, inside a metal garage (I am assuming), it may definitely show a different location. However, an AirTag is not "garbage". Lost and stolen items are found all the time with these types of devices. You also may want to verify the miles on the car.

I have one in my RV, inside a cabinet, under a metal covered roof (granted, not completely enclosed), and it shows me it's exact location within a few feet.

One thing you didn't mention is if you noted your car's odometer when you left the car, you can easily see how may miles / km have been added. If none, then you may have just gotten a false location information.

Never advertise you’re on vacation. Just good rule of thumb.

But…keep the application open for a bit and see if the tag recenters itself where it should be. It connects to other iPhones, iPads, etc (in the background, anonymously) and updates its location that way. It could be it just didn’t know where it was exactly at that moment.

In the FindMy app, you can put the device in “lost mode” and it will notify you when it’s location is found/confirmed or if it senses that it has moved to another location.

And make sure you have multiple screen shots at multiple times of the location of the vehicle as evidence. Keep the FindMy app open for a while, and see if it tracks the movement of the vehicle.