The broken back glass doesn’t actually void the warranty, but it is accidental damage not covered by the warranty. As far as the potential for repair or replacement is concerned, that has to be judged by the tech who actually examined the device, nobody here knows what was found on inspection.
It sounds like you would be content to accept the phone repaired with a broken back panel. However, there are several problems to this. First, it is almost impossible to reassemble with a broken back glass even if it doesn't break up further when it is dismantled. Second, Apple repairs carry a limited warranty, and there is no way your broken back will pass the water resistance required. Third, they have no wish to be sued when you cut yourself on the cracked glass after repair.
I believe the economic option is probably an exchange/replacement device. Modern smartphones have very few components and they have to be designed that way to get it to work in an acceptable size. Each component module is relatively expensive, so with the exception of the battery the cost of repair parts is usually way more than half the value of the device, plus the cost of labor to carry out the work. It doesn't take much to pass the cost of simply replacing, and from your description it sounds like the parts required might be the main electronics board AND a new back panel. That only leaves the display and the battery from the original phone.