Does a terrace roof take away a lot of light in the living room?

I would rethink the concept. Raffstores protect against views. You install the awning on top of your glass roof. Please believe that you will need this. Even with frosted glass, it will be more than warm underneath. Is the structure well ventilated? Because of grilling. And even if it is, think about it, you have the fat smoke hanging under the roof. After 2-3 years, it looks terrible.

I believe the basic assumption is wrong that you can't see dirt through frosted glass. In fact, you can see it very well. Perhaps a self-cleaning glass would be more sensible?

Frosted glass lets in more light than clear glass.

I consider the basic assumption wrong that one cannot see dirt on frosted glass. You can very well see it. Maybe a self-cleaning glass is more sensible?

Dirt on frosted glass is very visible. "Self-cleaning" glass only works with the appropriate slope. The awning is not the only alternative. I am thinking more in the direction of a motor-operated roof – as you find it, for example, in the gastronomy sector.