Support Request Logger for live views

[michalwarda]

Environment

Make sure you are using the latest LiveView and Dashboard versions before continuing.

• Elixir version (elixir -v): 1.15.2
• Phoenix version (mix deps): 1.7.7
• Phoenix LiveView version (mix deps): 0.19.4
• Phoenix Dashboard version (mix deps): 0.8.0
• Operating system: Fedora 38
• Browsers you attempted to reproduce this bug on (the more the merrier):
  It's not a bug.

Actual behavior

Currently the request logger functionality adds a cookie and logs http requests but does not log live view "requests".

Expected behavior

I suppose we can log also live view "requests". Especially taking into account the fact that when working with live view we make a very small amount of http requests and most of errors etc. are happening through live view requests.

I would be happy to try and code it but I have no idea where to start.