[chrome.displaySource] Session notification improvements

This patch provides several fixes and improvements (simplifications)
to the session life cycle notification mechanism:
1) The 'startSession'/'terminateSession' call completion callbacks are
invoked when the session is actually started/terminated and in accordance
with 'onSessionStarted'/'onSessionTerminated' events propagating (and as
per documentation).
2) The notification from the required sink is filtered out in browser process
avoiding unneeded IPC calls
3) Methods in mojo interface are renamed in order to improve readability

BUG=242107

Review URL: https://codereview.chromium.org/1674583002

Cr-Commit-Position: refs/heads/master@{#374929}
9 files changed