There are very few hidden battery e-bikes, Chris, and all those I know are over your budget. Nor is the "hiding" all that effective on most in my opinion, for example
Sparta and
BH E-motion both making the downtube expansion obvious, and both well over €2000.
IZIP made a similar one much cheaper, but then withdrew it and also discontinued the special batteries leaving owners stumped for replacements. That's an important consideration when buying of course.
I assume you will also want the motor to be discreet and quiet.
If you don't mind having a backpack/rucksack, a smart way is to carry a battery in that with a simple inline connector. That has the advantage that when leaving the bike, the battery can't be stolen! An e-bike stunt team run by Team Hybrid rode their bikes that way.
So a good option is to get the bike you like and add a discreet kit motor and backpack battery.