Bluetooth: Fixing potential mem leaks in bt_logger

During sluggish system state, threads can take more
time to execute after creation. This can lead to
race condition between log capture and log dump.

Made changes to ensure that log dumping to continue
even if log dump thread is scheduled with delay.

CRs-Fixed: 2057577

Change-Id: Icda6bebba1ae62dae2726af688677c61c771091f