What should I do when my Apple Watch Series 3 stuck on the Apple logo?

Did you already try to force restart your Apple Watch?

To force restart, press and hold the Digital Crown and the Side button together for about 10sec, until the Apple logo comes back again.

Has the battery ever been replaced by Apple?

Also have a look at the troubleshooting mentioned in this article:

If your Apple Watch won't charge or it won't turn on - Apple Support

You're welcome 🙂

To save some time, have a look at the troubleshooting here:

If you can't pair an Apple Watch with your iPhone - Apple Support