Clean concrete patio safely ?

I would use a pressure washer. They can be rented but you can purchase one for about $60. Great for all kinds of outdoor cleaning without chemicals...just water. Might even try a small plastic water concentrator on the end of your hose...this is just a screw on tip that creates a strong stream of water...about $2.

Dawn dish soap, vinegar (vinegar will kill the mold spores), a long handled stiff bristle push broom and a hose or pressure washer. Wet the area, squirt the dawn, brush brush brush, toss down a few cups of vinegar, Bush the surface again, then rinse. Vinegar can kill grass but mixed with the dish soap and gallons of water, it will be too diluted to harm anything. I do it a few times a summer to keep my patio clean. Mine is in blazing sun all day, but it is dusty here.

After pressure washing, I would recommend wet & forget outdoor to keep it clean. It will clean it eventually but it's a slow process with this product.

Try Bleach, a hard brissle brush and water it off? I’ve heard of people using Bleach for mold? Just a thought

I like Edie’s answer too, power washers are strong!

Oxygen bleach: https://www.stainsolver.com/clean-patio-stains-with-stain-solver/

It's harmless to plants/shrubs/grass, easy to use (no pressure washer required), and does a great job. It's a bit labor intensive, but that's a small tradeoff if you're trying to save your landscaping.

The vegetation is most likely causing your problem, particularly if the patio receives more shade than sun, is too wet, or the shrubs are mulched, which can result in "artillery fungus".