Whether it’s glass or plastic, there are polishes for both that should remove water spots.
My wife decided to remove some bugs from the windshield on her SUV using scotchbrite and I polished those out using a silica polish, iirc, and a Flex polisher.
Plastic should be significantly easier to polish.
You could first try some vinegar - or even better "heavy duty" vinegar. You can buy the HD stuff at your local box store. It's about 30% vinegar compared to household vinegar that is less than 5% vinegar. Saturate a cloth and let it sit for a few minutes.
When it comes to buffing, you probably were just low on elbow grease. Add more grease.
