Has the battery of your Apple Watch ever been replaced by Apple?
Depending on the age of your Series 6, the battery might be defective and the watch can not start up anymore.
If the watch does not charge anymore and start up automatically after being put on the charger for longer than 30min, this would be another sign for a defective battery.
You should get the watch either serviced or, given the age of the watch, consider buying a newer model.
If there is more damage to the watch, I would rather buy a newer model.

copied from: Apple Service and Repair for Apple Watch - Apple Support