Refactor adbd_auth to allow better testing

AdbdAuthContext is an opaque struct which is difficult to unit test.
This CL only moves code around to create an internal header, usable by
our unit tests.

Test: Manual
Bug: 421986516
Flag: EXEMPT (refactor)
Change-Id: I3dd0d4e587dc50b5a39a8205f418de406517338a