Move ContextualSearchManager self-invocation to SystemApi.

We will revisit making it a public API in the future.

Primary use case: allowing the Contextual Search app to
invoke itself after an initial invocation (i.e. while it's
already in the foreground).

Bug: 368653769
Flag: android.app.contextualsearch.flags.self_invocation
Test: Build and presubmit
Change-Id: I553cc38463ebc5b4401b14c5d2862c531c4cd133