Split public LLM provider code from internal #6732

Job	Run time
build-and-check	2m 38s
test-integration-packages/internal	1m 4s
test-integration-packages/billing	1m 6s
test-integration-common	49s
test-integration-cli	53s
test-.agents	39s
test-integration-web	48s
test-cli	55s
test-integration-sdk	1m 27s
test-common	41s
test-integration-packages/agent-runtime	40s
test-sdk	49s
test-packages/internal	52s
test-packages/agent-runtime	40s
test-web	56s
test-packages/billing	40s
	15m 37s

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