[omni] Make AssistStateManager SafeCloseable.

Saw presubmit error: https://paste.googleplex.com/6266943744507904#l=76
which is thrown at https://source.corp.google.com/h/googleplex-android/platform/superproject/main/+/main:packages/apps/Launcher3/src/com/android/launcher3/util/MainThreadInitializedObject.java;l=147-148;drc=1ce67a612220e7c9bd576d867cddf0fb74ccb866

Bug: 311356563
Bug: 330444720
Flag: legacy CUSTOM_LPH_THRESHOLDS disabled
Test: manual
Change-Id: I5fd28161756f10f0ec893f38c0abd51621fd36bc