Move VideoShareSession to third_party to remove bad cast in VideoShareManager

It was odd that we were casting and was causing some crashes. This CL makes
things work more as is typical in Dialer.

We previously did not do this because there are some parts of the
VideoShareSession which are not open-sourceable. Turns out we can simplify
those parts out of the interface.

Bug: 63523694
Test: existing tests
PiperOrigin-RevId: 161593028
Change-Id: I8f1379fc46f4e9d41413b731787dbf37e0901da9