Refactor IssueRecordingService to allow for Unit tests

Unit tests for IntentServices are not supported by the android framework. The
official recommendation is to refactor the business logic into a
separate class and then unit test that class.

Bug: 362571500
Test: Verified that these changes don't stop starting, sharing, and
stopping a trace from working using the record issue tile.
Flag: EXEMPT refactor for unit test

Change-Id: I56d2f4b0e7ccaafc2e60c7d97e09e41cff1a3b94