From scratch: Easily $100M. A contract just to spec out all the requirements of the system before writing a single line of code would cost around $1M.How much would it cost for Amtrak to start from scratch and create a totally new system based on proven technology used by airlines and Foreign rail systems?
The major problem with a major migration like this is not so much programming and replacing all the computers as much as it is transitioning to a new system, making sure all the new parts work and training everyone on how to use it.
As far as the car/room number not appearing in the app, I'm with @zephyr17 in saying it was a likely unintentional omission that happened as part of an upgrade process, or a conscious decision to leave it out. It may be that room changes or cancellations cannot be pushed to the app.
I do know I had to manually enter my latest reservation in the app by confirmation number, since it was rather complicated and created manually by someone in the reservations area.