Improve connection tests #12160

Job	Run time
analyze-other (python)	57s
analyze-other (actions)	53s
check-codeql-versions	10s
analyze-javascript (macos-14, linked)	9m 17s
analyze-javascript (macos-15, linked)	8m 27s
analyze-javascript (macos-15)	9m 47s
analyze-javascript (ubuntu-22.04)	4m 52s
analyze-javascript (ubuntu-24.04, linked)	4m 39s
analyze-javascript (windows-2022)	6m 17s
analyze-javascript (macos-14)	7m 16s
analyze-javascript (windows-2025, linked)	7m 6s
analyze-javascript (ubuntu-22.04, linked)	4m 55s
analyze-javascript (ubuntu-24.04)	4m 49s
analyze-javascript (windows-2022, linked)	5m 56s
analyze-javascript (windows-2025)	7m 13s
	1h 22m 34s

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