List of specific apps on my iPhone with Siri integration How do I see that list and the commands I can use for each app?
These two options may help, although it's not exactly what you're after.

One

When using Siri, at the bottom left of the screen, you'll see a '?'. If you tap on the question mark (?) Siri will list the apps you can use with Siri and tapping on an individual app will list some examples for you. 

Another way to access this screen is to just say something like "Hey Siri, what can you do?".

Two 

Go to Settings > Siri > App Support 

This will list 3rd party apps that you can allow to process requests via Siri. For example, if you have LinkedIn installed, it should be listed here.

Summary

As far as an exhaustive list of apps and how they can be used with Siri, I do think this is an unrealistic expectation. After all there are over 2 million apps currently in the App Store. How would you make this work in a practical sense? How could it be populated/maintained in a timely and useful manner? I'm not saying it'd be impossible, just that it's not really practical and the benefits would not justify the effort involved.

Instead, as developers take advantage of the Siri APIs the onus is really on them to highlight and 'sell' the virtues of their product. I know that's what I'll be doing.