If I'm understanding it right, the idea is that the DNS configuration for company-staging.com is identical to that for company.com - same IPs and servers, DNS provider, domain registrar.
Literally the only differences are s/company/company-staging/, all accesses should hit the same server with the same request other than the Host header.
Then you can update the DNS configuration for company-staging.com, and if that doesn't break there's very little scope for the update to company.com to go differently.
The purpose of a staged rollout is to test things with some percentage of actual real-world production traffic, after having already thoroughly tested things in a private staging environment. Your staging URL doesn't have that. Unless the public happens to know about it.
The scope for it to go wrong is the differences in real-world and simulation.
It's a good thing to have, but not a replacement for the concept of staged rollout.
Real "rugged" laptops are far too expensive for schools to buy by the dozen. Also, while robust against the environment they're not so much against deliberate vandalism or theft. The target market for those seems to be construction/industrial and similar, and of course the military.
All school laptop fleets I've seen are simply the cheapest thing they can buy in bulk, when it breaks provision a new one.
Then you can update the DNS configuration for company-staging.com, and if that doesn't break there's very little scope for the update to company.com to go differently.