I’d bet an elite variety fine fescue would grow just fine. You can get that stuff to grow in complete shade

I think this is generally just a bad idea. Vent straight outside if you must.

I’d look at doing a DIY filter with 2” HVAC filters and a big box fan.

Seriously. I paid about half of this for a prebuilt shed that was built to order, and has most of the same specs. Biggest difference is mine isn’t on a concrete slab, but I can deal with the step up into it.