On our old house the tarmac drive went tight up to the concrete garage floor, just a little lower, I guess to minimise water being driven into the garage. The drive sloped away from the garage.
Just poured our garage slab/floor and I went for level, but didn't achieve it. I need to self level a portion to stop liquid collecting at the back of the garage.
I guess that is DPC showing? In which case any concrete should end up below that anyway.
What is the channel?
Sounds like you may need a step at the fire door.