Non-functional refactor to move logic into RouterRecord

This allows a following CL that:
- Expands system routing permission.
- Allows to send route updates to a specific router.

This CL also removes an unused method.

Bug: 274894524
Test: atest CtsMediaBetterTogetherTestCases
Test: atest MediaRouter2HostSideTest
Change-Id: I8bc318e3ecee70b274ca260209d48b4fc76250a3
Merged-In: I8bc318e3ecee70b274ca260209d48b4fc76250a3