Audi TT horn blasts intermittently when I start the car

If your vehicle is equipped with air-bag, you could have damaged the spring reel under the steering wheel. I would suggest checking that first.

Yes, you definitely have damaged the spring reel. It has to be replaced and when installing, the correct procedures must be followed.

The spring reel has limited travel and when the rack and pinion was removed, turning the steering wheel excessively would break the cable inside the reel.

I am not sure about the connector reel but in the manual it is referred to as the spiral spring.

SPIRAL SPRING
Removal

1. Disable air bag system. Ensure front wheels are in straight-ahead position. Spiral spring is located under steering wheel.

2. Remove driver-side air bag module and steering wheel. Release steering column adjuster and position steering wheel in full downward and outward position. Remove tilt lever handle screws and tilt lever handle. Remove upper steering column cover screws and column cover. Remove lower steering column cover screws, bolt and lower cover.
Disconnect spiral spring harness connector. Release locking lugs and remove spiral spring. DO NOT turn or twist spiral spring after removal.

Installation
To install, reverse removal procedure. Ensure front wheels are in straight-ahead position.

CENTERING SPIRAL SPRING
If spiral spring is twisted, it must be centered before installation. From central position, spiral spring must be able to turn approximately 3 1/2 turns in both directions.

Your're welcome.

Have a nice day.