Title nit: "backup" means a second copy, "back up" is the verb phrase for moving backwards. Verb phrases get hyphenated for clarity when used as adjectives immediately preceding a noun. So this should be "back-up camera", not "backup camera".
I think this may be a case of language evolving/devolving and quite possibly an Americanism.
I'm British and to me backup means having a reserve or spare ready to use. You have a battery backup on your servers to step in when there is a mains problem, a photographer will have a backup camera, you backup you files regularly etc.
We would call this a reversing camera, for when you reverse your car using the Reverse gear. You can back into a parking space, or even just back up a little bit into a better spot.
One thing I'm seeing which irritates me is people are starting to call backing singers backup singers. They are not a backup the the lead singer, that would be an understudy, they are supporting like the backing on picture.
"backup camera", no hyphen or space, is at least popular enough to have a wikipedia entry.
https://en.wikipedia.org/wiki/Backup_camera
it is also used very regularly elsewhere, like government sites: https://www.nhtsa.gov/vehicle-safety/driver-assistance-techn...
or legal advice sites: https://thelegalguide.org/are-backup-cameras-required-all-ca...
or news sites: https://abcnews.com/US/cars-us-now-required-backup-cameras/s... https://www.reuters.com/article/business/consumer-groups-sue...
or automotive magazines: https://www.autoweek.com/news/a1892066/feds-backup-cameras-a... https://www.caranddriver.com/car-accessories/g44411856/best-...
it's safe to say that "backup camera" is perfectly acceptable.