Module: Add lock for started modules

The variable |started_modules_| is modified in one thread and could be
accessing in another thread which could cause race. This adds a lock to
prevent from it.

Bug: 393662321
Test: mmm packages/modules/Bluetooth
Flag: com::android::bluetooth::flags::fix_started_module_race
Change-Id: I7f0bb3af0268513adb78ba3bf940e1a16bf0d63b