Apple Watch stuck on Apple logo screen

If the Apple Watch has stopped responding,I suggest performing a force restart. Steps needed are found in the Apple Support article: Restart your Apple Watch - Apple Support

i.e. press and hold both the side button and Digital Crown for at least 10 seconds, then release both buttons when you see the Apple logo.

If you've completed that troubleshooting and the issue is still not resolved, Contact Support.

Click here > Contact - Official Apple Support

or phone numbers 

Click here > Contact Apple for support and service - Apple Support

I am experiencing the same problem on an Apple Watch Series 3. It just goes to the Apple logo and won’t boot. I’ve tried the force restart at least 20 times, allowed it to drain completely and tried again. No success. I scheduled an Apple genius appointment but their earliest one is 3 days away.

You will just have to wait 3 days unfortunately