refactor(cli): simplify chat input submission routing #4662

Job	Run time
build-and-check	3m 0s
test-integration-.agents	1m 3s
test-integration-backend	1m 5s
test-integration-cli	59s
test-integration-common	1m 2s
test-integration-packages/agent-runtime	58s
test-integration-packages/billing	1m 5s
test-integration-npm-app	58s
test-backend	58s
test-packages/agent-runtime	1m 15s
test-integration-sdk	1m 10s
test-npm-app	1m 11s
test-packages/billing	57s
test-packages/internal	58s
test-.agents	1m 0s
test-cli	1m 17s
test-integration-web	58s
test-common	57s
test-integration-packages/internal	1m 7s
test-web	1m 10s
test-sdk	59s
	24m 7s

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