Hello,
This section of the Apple Watch User Guide has some additional settings to check.
Turn on and wake Apple Watch - Apple Support
"Wake the Apple Watch display
By default, you can wake the Apple Watch display in these ways:
- Raise your wrist. Your Apple Watch sleeps again when you lower your wrist.
- Tap the display or press the Digital Crown.
- Turn the Digital Crown upward.
If you don’t want your Apple Watch to wake when you raise your wrist or turn the Digital Crown, open the Settings app on your Apple Watch, go to Display & Brightness, then turn off Wake on Wrist Raise and Wake On Crown Rotation.
Tip: To temporarily prevent your Apple Watch from waking when you raise your wrist, use theater mode.
If your Apple Watch doesn’t wake when you raise your wrist, make sure you selected the proper wrist and watch orientation. If your Apple Watch doesn’t wake when you tap the display or press or turn the Digital Crown, it may need charging."
Though it's not mentioned here an Apple Watch will also not wake from raising your wrist when Low Power Mode is enabled.
I hope this helps.