Is it normal for paint to still look dull after a good wash?

What you're feeling is bonded contamination sitting on top of the paint, plus probly a dead layer of oxidized clear coat that washing alone can't touch. Totally normal after a couple years outside. You didn't mess anything up, you just finished step one of about three.

The rough sandpaper feel is things like tree sap mist, road tar, industrial fallout and general grime that's glued itself to the surface. A clay bar is exactly the fix for that. You spray on some quick detailer or soapy water as lubricant, then gently glide the clay over the panel in straight lines. Don't press hard, let the clay do the work. You'll feel the surface go from gritty to glass-smooth, and it's honestly satisfying. When the clay face gets dirty you fold it over to expose a fresh spot. If you drop it on the ground, toss it, no exceptions, otherwise you'll grind grit into the paint. Clay is safe on healthy clear coat if you keep it lubed. Rubbing through clear coat comes from aggressive machine polishing or dry sanding, not gentle hand clay work.

After claying you'll likely notice the haze even more clearly, because now you're looking at the actual paint condition rather than grime. That dullness is oxidation and light swirl marks. On a daily driver you can fix a lot of it by hand with a polish or cleaner wax and some elbow grease. Work panel by panel with a foam applicator pad, small circles, moderate pressure. You're not trying to cut down to bare metal here, just level off the dead top layer. For a first timer, a cleaner wax is forgiving since it polishes and protects in one pass. Then finish with a proper coat of wax or a sealant to lock it in. Two coats a few weeks apart helps on a car that lives outside. Given that your coupe sat in the sun for years, don't expect mirror gloss in the deep scratches, but a good clay, hand polish and wax will get you a geniune shine back on a driver. It might take a second weekend rather than one, but the paint on those old Probes cleans up really well if the clear coat hasn't failed through to the base color.

Reading this with interest because I'm in a similar spot with my dad's old pickup that sat under a tree at his place for ages. I washed it last month and got the same letdown, dirt gone but the hood still looked chalky. Never worked up the nerve to try clay yet. One thing I'm still unsure about, how do you actually tell when the clear coat has failed through to the base color versus just being oxidized on top? I keep staring at the roof on mine wondering if it's saveable or if I'd be wasting a weekend on paint that's already gone.

I'd push back on the cleaner wax suggestion though. If the paint feels like sandpaper and looks chalky, a cleaner wax is way too mild to touch that level of oxidation. I used one on my old wagon and it did basicly nothing, just smeared wax over dull paint. A dedicated polish, even applied by hand, is what actually levels that dead layer off. The cleaner wax approach only works when the paint is barely faded to begin with, which clearly isn't the case here. That said the guy is right that hand polishing is slow going. I did my hood and roof one afternoon and my arm was cooked by the end.