Apple Watch 3 still not giving sleep levels data

I hate to be the bearer of bad news but Sleep data is for devices running watchOS 9 and your Series 3 watch can't be updated to that OS.

It's because the Series 3 doesn't have the necessary hardware (sensors and memory) to support watchOS9.

The new Watch SE Gen 2 would be an affordable upgrade from the Series 3 but... You need to have a minimum of an iPhone 8 that is running iOS 16.