refactor(.agents): improve tmux session management with JSON output a… #5489

Job	Run time
build-and-check	2m 42s
test-integration-packages/internal	39s
test-integration-.agents	48s
test-common	40s
test-integration-packages/billing	2m 50s
test-integration-packages/agent-runtime	39s
test-integration-web	46s
test-sdk	44s
test-web	46s
test-packages/internal	54s
test-packages/agent-runtime	56s
test-.agents	47s
test-packages/billing	39s
test-integration-common	49s
test-cli	1m 20s
test-integration-cli	49s
test-integration-sdk	46s
	17m 34s

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