My Apple Watch's volume control is not working after 10.4 update

Use Watch Settings, Sounds & Haptics and adjust the slider by tapping, or tap slider and rotate digital crown.

If that doesn’t work then start basic diagnostics by force restarting the Watch and paired iPhone at the same time:-

Force restart the Watch

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. 

Then while Watch is restarting, force Restart the paired iphone   Force restart iPhone – Apple Support (UK) 

Test it for a suitable period depending on the nature of the problem.

If it is still misbehaving...

Unpair and set up again, takes about 20 minutes.

 Unpair and erase your Apple Watch – Apple Support (UK) 

Set up your Apple Watch – Apple Support (UK) 

If no remedy, unpair again and setup without restoring the backup. You will lose little except Faces and some settings. This is a good remedy when you have lost Apple included apps but you can't find them in App Store, eg Workout app.

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

and or Genius Bar Reservation and Apple Support Options - Apple

It isn’t the update.

Restart it.

How to adjust various sound volumes on Ap… - Apple Community

You certainly did not ready user tip where the first line is "There are at least three categories of Apple Watch sound where you can adjust volume."

If you are not prepared to say which one then I am not prepared to waste my time.

Umm goodbye

It might help if you said which volume is not working

There are at least three of them, the detail is in my responses, Pick one and work on it.

For some of us, it’s just not working. I read the details, read the user tips. Just doesn’t work 90% of the time. No need to be rude.

Which volume control? No need to be vague like the author.

For music. Any app.