Why does my build plate sit at an angle after a print finishes?

The hang at the end is normal, that's just the finish routine. Once the last layer is done the machine parks the plate over the vat in a tilted position so resin drains off the print and back down instead of dripping everywhere when you lift it out. Some machines sit like that for a while or even give the plate a little nudge before settling. If the screen says the print finished, just let it be. It's not stuck, it's not failed, it's literally just draining. On mine I can set how long it stays there in the settings, yours probaly has something similar if you dig around, but there's no harm in leaving it as is. On the supports, I'd actually keep them dense for now and work on making them easier to remove rather than thinner. The trick is usally adjusting the contact point size and depth rather than cutting the number of supports. Smaller tips mean less scarring on the model and less grip to fight, but you still keep plenty of them so nothing sags or detaches mid print.

The mistake people make going thin too early is dropping the support count on a bigger model, then a corner lets go around the middle of the print and you end up with a failed blob fused to the FEP film. That cleanup is way worse than a few stubborn contact points you have to snip off.

What I do is start with the slicer defaults, run a few prints, then nudge one setting at a time. If the supports came off hard but the model surface underneath looks fine, reduce the tip thickness a touch. If marks are showing on the surface, go back up. If everything held and you want faster prints, you can start spacing them further apart gradually.

Also, since your first print came out clean, don't be surprised if you can trim the bottom exposure down a bit later. Tight but not welded to the plate is what you're aiming for, and it makes removal easier too.

Same expirience with the end wait. Mine sat tilted for a couple of minutes the first time and I hovered over the stop button sure it had locked up. Now I just walk away and come back when it beeps. Can back the support advice too. I kept the density at default and only shrunk the tip size one step, and that alone changed everything. They snap off with my thumbnails now and barely leave a dimple. Been thru maybe a dozen prints since, including one tall hollow piece, and nothing has let go yet.

Update: took the advice and just walked away during that tilted wait instead of staring at it, and sure enough it beeped and released on its own. Also thinned the support tips down one step on my second print and they popped off way easier with no failures. New thing I noticed though, the plate had a thin film of cured resin on it after. Is that normal or am I leaving it in the vat too long after the beep?