I’ve sanded down to where the wall feels even but now the patch’s showing what should I do next?
Part of the problem may be sanding technique. It appears that you have used a soft pad or bare sheet. You need to use a rigid block to prevent sinking into soft spots.
Apply another coat of patch material, and taper it out a bit further. Proper drywall work doesn't involve much sanding at all, so make sure to use a wide knife or trowel at a low angle to create a flat, smooth repair. Sanding should take mere seconds.
It's not uncommon to see what's under the bare mud patch (I sometimes use a yellow fiberglass mesh tape which sticks out from the white mud). Seeing underneath isn't an issue. Once you paint it, you can't see it anymore.
The larger issue is you don't want to feel what's underneath. Once it's painted, you'll notice the shape on the wall. Your best bet is to take some spackle and layer it around the sides. mound it up perpendicular to the edge of the patch, then run it down the side. After it's dried, sand it with something minor (like 200 or 220 grit sandpaper). Just enough to smooth it, without taking too much off.
If you can still feel it, rinse and repeat until you can't.
That looks like a 5" or 6" patch. I would suggest using mud or spackle and taking it out to half the width of the patch, so about 3 inches around the edges. Use more than you think you need and try to feather it at the edges. Then use a hard sanding block to smooth the patch, texture and paint. You should be in good shape at that point.