8mm double wall bronze light transmission is about 30%. 6mm is about 50%. Clear is around 80% for all thicknesses. Greenhouse design shoots for 80% to 90% transmission. Three-wall clear is about 75% and that is considered low enough transmission to limit type of plant or to long growing season.
There's some research that suggests that you give up 1% yield for each 1% of lost light transmission. There are other factors, like orientation relative to sun path. But high light loss is going to be felt, all things being otherwise equal.
My greenhouse is covered in heavy plastic panels that are heavily matted from exposure. My lux metering result isn't bad, but I still provide supplemental lighting timer controlled to about the daylight period.
I agree that shade cloth is the way if absolutely have to cut back on sunlight in summer. It's no better than tinted material, but it can come down in darker seasons when the heat is not a bad problem. But if I had power, I would actively ventilate, which if done with sufficient vigor will keep the interior at about ambient outdoor air temperature.
Since you're building it, you have all sorts of options to avoid overheating, like wide lend doors or walls.