Apple watch will not stay charged after recent software update

First you can check for damaged or -discharging battery... 

How to check your Apple Watch battery fo… - Apple Community

Force restart your 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 Force Restart the paired iphone   Force restart iPhone – Apple Support (UK)

Try it for a day

Then make sure to turn off background app refresh and  check walkie talkie is not accidentally turned on. 

Try it for a couple of days especially if you sync photos to your Watch.

Unpair the watch and then pair it again. 

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

Set up your Apple Watch – Apple Support (UK) 

 If it still discharges unpair it and pair it again without restoring the backup. 

Check that the iPhone is not using any security apps or VPN that can affect apps on the Watch. You don't need any of them and they can be incompatible with iOS16 on the phone. 

see also 

Apple Watch - Battery - Apple (UK)

Batteries - Maximising Performance - Apple (UK)

If you checked for leaky battery , and set it up as new then you had better take or send it in for repair. That is not normal.

Apple Watch Service & Repair - Apple Support

or

Genius Bar Reservation and Apple Support Options - Apple