You can do both, typical rooftop solar installations typically don't cover the majority of the roof. Make the rest reflective and/or make it a space for people. Rooftop area has some of the greatest views in any city. Kinda crazy that we don't use it as space for humans and greenery in most cases.
I want to point out that to optimize for temperature reduction, you want to minimize absorption while maximizing thermal radiation. This says you want the surface to be reflective at wavelengths below some cutoff, but perfectly emissive (that is, black) above that wavelength. (Actually it's a bit more complex, because the atmosphere emits IR in some bands.)
Some work on surfaces of this kind have shown promising results, being able to fall below ambient temperature even in full sunlight.
Rooftops are great, we have a 100m2 rooftop terrace and kids love it. But I had no idea how hot it gets. To the point where I don’t even step outside during those heatwaves. When the offical temperature was 36C we had in fullsun above 46C and the concrete panel was too hut to wall barefoot. So my take is that in dry/hot areas rooftops are just unliveable.
Definitely depends on the area but there are flooring options that stay cool, and if really hot weather is a common issue, a misting system can keep things surprisingly cool at the cost of some water use.
