Prevent sending partial CLCC responses

If a new headset connected while sending CLCC responses,
there are a little chance to send partial CLCC responses to the
newly connected device.

This CL prevents those cases.

Bug: 215674669
Tag: #refactor
Test: atest CtsBluetoothTestCases HeadsetServiceTest
Change-Id: Iafc39714226772d582578a5d33b1ba74037084c3