Trying to install available apps to apple watch

I tested installing a third party spp smd still no double-click but it did stall until I checked my Watch and connected it to wi-fi

If yours is still connected to wi-fi and still have problems....

First make sure you are not using VPN or VPN adblockers or security apps on the iPhone. They can wreak havoc and protect nothing.

Start 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) 

You may also want to make sure the software on the watch and iphone  are both up to date to the same level. Updates are in pairs. eg iOS16.6 and watchOS 9.6 go together

Update your iPhone or iPad - Apple Support first then

Update your Apple Watch - Apple Support 

Test it for a while. 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 and setup without restoring the backup. You will lose little.

Thr normal process is on iPhone, Watch app, My Watch tab, look at the list of available apps and tap install.

No double tap required

Thats great, glad I could help.