bta_gattc_api: Improve queueing messages

This patch fixes, possible lost of the GATT message, because of the GATT
being busy with handling other request.

Bug: 249431973
Test: atest BluetoothInstrumentationTests
Test: manual testing GATT
Tag: #feature
Merged-In: I1575b75d172a71f6d7c001441b335d5873f56f57
Change-Id: I1575b75d172a71f6d7c001441b335d5873f56f57
(cherry picked from commit db0645b8)