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Use `setup-codeql` logic for finding release assets in `start-proxy` #13627

Job	Run time
analyze-other (actions)	52s
check-codeql-versions	18s
analyze-javascript (macos-15-xlarge)	2m 52s
analyze-javascript (ubuntu-22.04)	2m 56s
analyze-javascript (windows-2022, linked)	5m 1s
analyze-javascript (ubuntu-22.04, linked)	5m 8s
analyze-javascript (macos-14-xlarge, linked)	2m 52s
analyze-javascript (windows-2022)	6m 3s
analyze-javascript (ubuntu-24.04, linked)	3m 51s
analyze-javascript (ubuntu-24.04)	3m 30s
analyze-javascript (windows-2025)	6m 17s
analyze-javascript (windows-2025, linked)	7m 2s
analyze-javascript (macos-15-xlarge, linked)	3m 7s
analyze-javascript (macos-14-xlarge)	3m 6s
	52m 55s