A car body shop should be able to spray a bike for you or leave it carbon with a clear coat for protection.
Modern paints don't really need a clear coat, that's more for aesthetics... that deeper, wetter look.... or to add metal flake (which reduces longevity the most) ....a clear coat over a color would add unnecessary weight.
The clear coats (with. UV protectant) ARE crucial for any carbon frame that won't be painted a color... that naked or matte carbon MUST have UV protection.
But if you paint it a color or colors with modern high-end paint -- and I'm thinking a nice two-part linear polyurethane, for example -- there is no need for additional coatings for UV or longevity. In fact, the clear coat is often what fails first on a car, you have probably noticed.
And these LPU type paints have huge longevity now and don't need waxing (in fact, its a bad idea as it abrades away the top smooth, element-protecting part of the paint and REDUCES longevity.
One issue, though, is weight. Paint can be pretty heavy and people who paint cars don't really have to worry about that. Talk through what you want with them, which is to ghost on an initial tack coat as lightly as they can, then after than apply the minimum number of coats it takes to properly cover and color the frame.
You do NOT want that extra insurance coat I tend to shoot on my own vehicles.
That bike will spend its days inside and the paint really won't be subject to the elements etc.
Read a technical article once on an alloy 40-foot yacht mast that they wanted to get weight out of and they stripped off ALL the paint and ghosted on the lightest, thinnest coat of white they could and saved several pounds...