floss: Refactor lock usage for advertising in btclient

To use the lock for advertising safely and concisely, key changes in
this patch:
+ Acquiring lock once for correctness if appropriate.
+ Avoid borrowing context as mutable from an immutable borrow,
  required information is collected in advance and then passed
  to the D-Bus call which requires a mutable borrow.

Bug: 255863017
Tag: #floss
Test: build.py --target test
Test: manaul test on volteer with btclient and btmon
Change-Id: I7f4c1fc6f3fb0732ba5d204cfdf57b2a48763ece