This is a very viable marketplace idea, but I would not position it simply as “Uber for TV repair.” The difficult part is not building the Laravel + Flutter software. The difficult part is building the operational, trust, logistics, pricing, payment, technician-quality, and dispute infrastructure around it.
The client already has a strong starting advantage: 5 shops + 35 technicians + existing repair demand. That gives you the seed supply for the marketplace, which is usually the hardest part of this kind of business.
Think of it as a managed repair marketplace.