Paid big money for a paint correction so why does my car look worse in sunlight?

Dark grey paint in direct sun is the most honest lighting there is, and it will show every defect the shop lights smoothed over.LEDs at the shop are usually positioned to make the paint look its best, so don't beat yourself up for being impressed in there. Sunlight angled down the panels is where the truth comes out. That said, what you're describing sounds like real scratches, not just haze. The fingernail test is the honest answer here: if you can catch a nail on it, that scratch is sitting well down in the clear coat, and a standard correction doesn't remove those. Polishing only shaves off a small layer of clear. A true defect-removal job on scratchy paint means multiple stages, and most shops quoting under a grand for correction plus a coating are doing a single polish pass. That pass makes everything glossier and cleaner, which paradoxically makes the remaining deep lines stand out MORE, because now the paint around them is flat and reflective instead of swirled and hazy. The scratches were probably always there. Your old wax or the haze was hiding them.

Go back to the shop. Bring the car in daylight, park it outside their door, and walk the panels with whoever ran your job. Ask them straight up whether those nail-catch marks were flagged before they started. Good shops will show you a before shot or point out exactly which spots they called unsafe to fully correct. If they communicated that poorly, that's on them and most reputable places will offer to spot polish a few of the worst ones. Just know that anything they fix after a coating means re-polishing that spot and re-coating it, so they may not be thrilled, but a shop with a good local reputation will usually work with you.

Also worth checking how you're washing it now. Fresh scratches on freshly corrected paint usually means something in the wash process, a dirty mitt, a bad drying towel, or an automatic brush wash somewhere in between.

The wash process point is the one I'd hammer on. I had a similar wake up call after paying a mobile guy to correct my black truck, and I messed it up myself within a month by reusing a drying towel that had picked up grit from the driveway. Couldn't see it until the sun hit the doors. Now I keep wash mitts and drying towels seperate in sealed bags and toss them if they ever hit the ground. Went from fresh scratches every couple weeks to basially none. It's a boring fix but it works.

Lesson I learned the hard way on my old silver coupe: always do the walk-around with the shop before they hand you the keys, and take pics in thier light AND outside in the sun before you pay the balance. Any decent shop will let you do that. Also, if those marks were there before, they'll likely show up in whatever before photos the shop took for their records, assuming they do that. Worth asking to see them. I've found most shops are way more reasonable about a touch-up pass when you show up calm with photos instead of heated.

Your gut about somthing masking the marks isn't crazy. Back in the day shops woud finish with a glaze full of fillers under a coat of wax, and it made butchered paint look decent for a few washes. Polish oils can do the same thing even without a glaze. If some of those lines look worse after a wash or two, that's the oils gone and the fill gone with them. Worth asking the shop what their finishing step was. A coating over filler polish is a short-lived party. Old trick for checking at home: park so the sun sits low down the panel and look through a cheap plastic baggie over your hand, shows the truth better than any light bar I've ever owned.