Problem
Standard quick release has only two wires dedicated for the standard horn button:

For mounting other buttons onto (or underneath) the detachable wheel itself, four options:
Solutions
- Attach a connector separately from the quick release, branching out from the steering column in a parallel harness into the steering wheel with pins for all the buttons’ wires and route them inside the steering wheel casing, with sufficient buffer length to allow for safe rotation of the wheel - like below but imagine a much thicker wiring harness: mounting like the 10G wire in How the Horn Wiring Works - NRG Quick Release, positions of connector, parts list like: (2) We Have a Racecar Steering Wheel!!! 2 Step and Horn Buttons Installed! - YouTube Steering Wheel Cord Quick Release: One Cord, 4 buttons, and Quick Release. Monocord Pro by Motion (youtube.com), (2) HOW TO MAKE A DIY AUDI DTM STEERING WHEEL - YouTube and PCB arrangement, if required like HOW TO MAKE A DIY AMG STEERING WHEEL (youtube.com)

- Make a separate bracket containing the required buttons (under 5 only) onto one side of the steering wheel with a seperate (thin) wiring harness, somewhat like this: Quick Release Steering Wheel Walkthrough w/ Cruise Control and Horn (youtube.com)

- Use a wireless setup which might involve embedding a smaller MCU inside the steering wheel casing itself and some traffic with the telemetry mounted as a shield on a keyboard numpad PCB, like in https://www.youtube.com/watch?v=SoCb3fSsh_w

- Embed a bracket containing the buttons into the steering column itself (if there’s a plastic casing around) right underneath the steering wheel like the indicator switches in this:

Summary
To summarize: 1) parallel wiring harness A) with big connector embedded into steering wheel or B) going directly into a smaller bracket attached to the steering wheel itself; 2) attach brackets to steering column right underneath the detachable wheel itself; 3) wireless no frills setup at the cost of telemetry traffic & reliability
Steering Wheel Manufacturing: Carbon Fiber F1 Style Steering Wheel- Stage 13-Part 1 (youtube.com)
Foregrip manufacturing: Carbon Fiber F1 Style Steering Wheel- PART 2 Stage 13 (youtube.com)