My iPad won’t rotate even after I lock and unlock the screen

Force Restart your iPad and see if that fixes the issue.

• Pad models with Face ID: Press and quickly release the Volume Up button. Press and quickly release the Volume Down button. Then press and hold the Power button until the device restarts.
• iPad with Home button, iPhone 6s or earlier, and iPod touch (6th generation) or earlier: Press and hold both the Home and the Top (or Side) buttons until you see the Apple logo.

It won't rotate at all, or it won't rotate in an app?

I've had that happen and a simple restart cleared it up. It's worth a try, very easy to do.