Hi gfuji,
Welcome to Apple Support Communities. It sounds like you've tried some great troubleshooting steps so far. First, make sure that Schooltime is set up for the correct hours and hasn't been exited. The guidance from Get started with Schooltime on Apple Watch - Apple Support can help.
If everything looks good, restart both the Apple Watch and iPhone. Make sure they are both up-to-date as well. If needed, reference the articles below.
Restart your iPhone - Apple Support
Update your iPhone, iPad, or iPod touch - Apple Support
Restart your Apple Watch - Apple Support
Update your Apple Watch - Apple Support
If the same continues, unpair the Apple Watch using the steps below, then set up again.
"How to unpair your Apple Watch from your iPhone
- Keep your Apple Watch and iPhone close together as you unpair them.
- Open the Apple Watch app on your iPhone.
- Go to the My Watch tab and tap All Watches.
- Tap the info button next to the watch that you want to unpair.
- Tap Unpair Apple Watch.
- For GPS + Cellular models, choose to keep or remove your cellular plan.
- If you want to pair your Apple Watch and iPhone again, keep your plan.
- If you don't want to pair your Apple Watch and iPhone again, remove your plan. If you aren't going to pair with a different watch or iPhone, you might need to contact your carrier to cancel your cellular subscription.
7. Tap again to confirm. You might need to enter your Apple ID password to disable Activation Lock. Before erasing all content and settings on your Apple Watch, your iPhone creates a new backup of your Apple Watch. You can use the backup to restore a new Apple Watch. After your Apple Watch unpairs, you'll see the Start Pairing message.
8. Set up your Apple Watch again."
If you previously used Family Setup, you'll want to use the guidance from Set up Apple Watch for a family member - Apple Support when you get to step 8 above.
Have a great day!