There are plenty of photosynthetic molecules on Earth besides green chlorophyll. Depth in the ocean is partially responsible because different colors get absorbed by depth. It's an easy analog for deeper atmospheres. Chemistry allows chemosynthesis in the depths of the deep ocean without visible light at all, but heat is light: infrared. Humans photosynthesize also, making vitamin D. Even the dyes in our eyes are a type of photo reaction analogous to photosynthesis. Green predominates on Earth because of the color of our sun for which the bell curve peaks in the part of the spectrum that provides lots of what would be green in a radiative spectrum (I think I got the term right, but don't quote me).
As for atmospheric depth, we get blue scattering in the sky because sunlight only travels a short distance through the air, but orange and red when it travels all the way from the horizon, which incidentally strips the energetic wave lengths that readily support chlorophyll synthesis. Red dwarf and orange sun worlds might not support chlorophyll at all. Brown dwarves might support only heat cycles or heat accelerated chemical gradient synthesis. Too thin an atmosphere lets in UV, which is destructive as it is too energetic, and too thick will freeze a world or make something like Venus.
As for mixes, nitrogen is clear unless it is chemically activated to make smog. CO2 is not entirely clear to infrared. Ozone blocks UV but is highly reactive and dissipates. Helium and hydrogen I think are clear, but as others have stated it tends to get stripped by solar wind and would require a super earth's gravity to last billions of years, which might mean your world is mini-Neptunes and not conducive to life. Steam can be an atmosphere or a major component and will affect visibility and synthesis, hot clouds essentially. Impurities like on Venus certainly would affect synthesis but not from occlusion. Let's skip discussing worlds with vaporized iron atmospheres.
I would suggest lots of Google searches for types of photosynthesis and things like life in deep ocean heat vents, geyser pools, red tides, stromatolites, blue green algae, and speculations on astrobiology.
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