Allow automatic landscape mode switching on my iPad

Try rebooting your iPad. You don't say which iPad you own, but if yours has a home button: Press and hold BOTH the power and home buttons at the SAME time (keep holding past the swipe to power off) until the Apple Logo appears, then let go.

If you own iPad Pro 11 or 12.9 with FaceID, the procedure is different.

So when you rotate your iPad, the screen does not rotate? If that is what you are saying, on your iPad screen, swipe down from the top right hand corner to open Control Center. Look for an icon with lock surrounded by a circular arrow. If it is locked, it will be red. Tap it turn on screen rotation.

Note: Not ALL apps rotate. It is up to the app developer to program rotation into their apps.

Rebooting often cures the oddest little things. Glad it worked for you!