how can I see if my SE is IOS 16 compatible?

iOS 16 Preview - Apple

near the bottom of the page it shows devices.

Your details show an iPhone 5s running iOS 12. If that's true, you can't run anything newer.

If you can't currently update to iOS 15, then you will not be able to update to iOS 16

The original iPhone SE is not compatible with ios 16. The 2nd and 3rd generation SEs will be.