You don't have to because fabric paint isn't like regular spray paint that goes all over the place, but you'd be able to paint hard to reach spots if you took out at least the front seats. Check out some YouTube vids to see what would work for you.
Laundry soap mixed with water in a spay bottle, spray on heavy wipe around with a rag, vacuum with a wet dry shop vac, I have done cars with a garden hose and shop vac, mine has black leather but the head liner looked about like yours. Like new now.
Every time I've ever used resolve to clean up some mess (or a pet accident), I always thought that it just ended up making it smell worse. It would clean up the stain, but that stuff just has a really weird smell that tends to linger.
Is the interior still wet? Do you have access to a garage, so you can leave the windows down?
TBH, once a year I pull my interior and clean it all.
I use the air compressor to blow out the dust and loosen the big stuff and my shop vac to clean as much as I can. Then I go after the rest with soap and water. I wash my interior just like I do the exterior. Standing water, I just grab the shop vac again.
So long as you avoid the electronic bits you're fine washing the interior.
Carpet and seats get hit with a hose and detergent. Shop vac to get excess water out. Sun dry.
Headliner you have to take more care with. Excessive water will pull it loose. So light water and detergent works best here. Sun dry.
All the interior panels can get wet with little to no damage (within reason). Don't dunk them in water, just spray.
The rear carpeted sides, you don't want to get these soaking wet. Just damp enough to wash dirt out is good. They loose shape/rigidity if they get too wet.
It'll take you the better part of a weekend to clean and dry everything. But once done, it's like a new car again and all the smells will be gone, besides that of the detergent you use.
It's really not that hard to remove everything. I can have a car gutted in about an hour and half.
And it's kinda scary all the crap that accumulates where you can't see.
I totally agree with the last post short of the headliner, I did use my vacuum and water on mine, the vacuum brushed out the scratches and the water/soap cleaned it. Agreed though that it could pull it down. In my case when you buy a car from a crack head you clean everything!
You need to pay a professional to fix this. Whatever made you think that outdoor furniture cleaner would be appropriate for vehicle interior is beyond me...
Pay to get it fixed and immediately install seat covers and floor mats, duh.