when I bought some high-quality exterior grade Behr paint (primer+paint in one) from Home Depot, there was a mistake in the order and I got a whole gallon for free. So, guess what I used to paint the inside of the coop & ramp!
But, first, let me say, that no, you don't have to paint anything.
My personal opinion, now. I had read that using exterior grade paint inside will help with the spray down. My coop isn't even 6 months old yet so I haven't had to spray it down yet. But, I have noticed that it covered up all the splintered wood fibers & tiny crannies where mites or chicken ticks can hide in. (Being new to chickening, I'm really paranoid about all of these scary things you hear.) So, in retrospect, I would do it again! Wood is a very absorbent surface, but painting it with a thick, waterproof paint makes it seem more like a solid surface. The fumes are gone after a few days and I have noticed zero reasons why painting the interior may not have been a good idea.
I used the same on the plank to make washing off the poop easier. Again, I haven't sprayed anything down, but the rain has washed it off on its own. So, I vote for a yes to exterior-grade paint on the ramp too! I think our ramp is steeper than yours and the chickens have mastered it just fine. Yes, I do have the ladder rails on my ramp.
On a side note, the paint I used was a creamy bright white color that I'd used on our door. I don't recommend white colors because they show all the poopy stains and dirt! But, a bright neutral color would be a great bet!
These pics don't show anything well, but you can see the ramp & the back of an interior door.
(this chicken has weird skin & i was taking a pic of its foot so ignore its poor, sad feet.
good luck! And, welcome to byc!