feat(test): track when running process ends during bitcoin-cli stop

[bitcoin-tools]

Refactor Bitcoin Core stopping logic to improve clarity and reliability.

Describe the changes and your approach

Pull Request Sign-Off

• I reviewed and approve of my changes.
• I checked of the automated test results for any irregularities.
• If appropriate, I manually tested the code changes on my local environment.
• If appropriate, I considered changes to the README or test documentation.

[bitcoin-tools]

+ bitcoin_pname=bitcoind
runner            3221   0.0  0.1 435304560   5024   ??  S<    2:23PM   0:00.01 caffeinate -sw 3211
+ '[' bitcoind = bitcoind ']'
+ sleep 2
+ bitcoin_stop_sleep_elapsed=8
+ ps aux
+ grep 3211
runner            6362   0.0  0.0 435298848   1488   ??  S<    2:26PM   0:00.00 grep 3211
+ '[' 8 -ge 3600 ']'
++ ps -p 3211 -o comm=
+ bitcoin_pname=
+ '[' 1 -eq 0 ']'
+ handle_error
+ handle_exit
+ kill_tail_process
+ kill -0 1828
+ '[' false = true ']'