The Apple Watch screen lights up when you raise your wrist, but you can disable this feature. To do this, go to the Settings app on your Apple Watch, then go to "Display and brightness" and deactivate the "Turn on when wrist is raised" option.

Regarding the option to leave the screen on without it going to sleep, you can configure how long the screen stays on after you touch the screen or press the Digital Crown. You can choose to keep the screen on for 70 seconds. However, the "Always on screen" function is not available on the Apple Watch SE .