Why does my projected clock image look so washed out?

The haze is mostly your matte print, yeah, but not because it's matte. Flat black is actualy what you want inside a light box, matte or not, because it absorbs light instead of bouncing it around. The problem with raw PLA is that black filament often isn't very black, and the layer lines give a slightly shiny sheen that scatters light right back toward the lens. What worked for me was a few coats of cheap flat black spray paint inside the case, plus a strip of black felt around the lens edge where light likes to sneak past. Made a night and day difference on the grey fog. Also check the gap between the OLED and the lens barrel. Any light escaping around the edge of the display instead of going through the glass will light up the inside of the tube and get projected right along with your digits. Black foam or felt taped around the display edges kills most of that.

On focus, part of it is the lens. Cheap 50mm lenses usually have noticeable chromatic aberration, so the edges of digits never get truly razor sharp, expecially near the rim of the glass. That said, it helps to find the real focal length instead of trusting the listing. Take the lens outside, focus a bright window or lamp onto a wall, and measure the distance where the image is sharpest. That's your number. Then set your display-to-lens distance based on that and the throw distance to your ceiling, using the lens equation, rather than eyeballing it. One more thing that helped mine: bump the display brightness way up and let the room darkness do the rest. A dim room makes even a mediocre projection look crisp because your eyes aren't fighting ambient light.

I fought the same fog on a little projection build and the thing that finally fixed it wasn't paint at all, it was a hood. I rolled a short tube of black cardstock and stuck it out past the lens, maybe an inch or so. Any light bouncing off the ceiling or the lens face was getting back into the optics and washing everthing out. Cost me nothing and the digits went from grey blobs to actual black-on-white looking numbers.

I dunno about the brightness advice. Cranking an OLED to max for hours is asking for burn-in on the digits, especially when the same few pixels are lit 24/7 on a clock. I ran one flat out for a couple months and now you can see a ghost of the time pattern when the display shows anything else. A dimmer panel in a darker room looks about the same anyway. Might be worth finding the lowest brightness that still projects well instead of the highest one that doesn't cook the panel.

One thing I'd add: check that the OLED glass is dead parallel to the lens. Mine was tilted a couple degrees and the top of the digits was always soft no matter what I did with focus. Wedged it square with a bit of foam and it snapped into shape. Also try cleaning the lens itself, cheap ones ship with a greasy film on them that fogs everything up. Isopropyl on a cotton pad, gently, fixed mine.

Another trick from way back when I was messing with overhead projector panels and such: put a small aperture stop in front of the lens. Cut a hole in some black card a bit smaller than the lens diameter and tape it over the front. You lose a little brightness but the outer part of any cheap lens is where the slop lives, and masking it down makes the image noticeably cleaner. Worth sliding the card around a bit to see how much you can crop before it gets too dim.