docs: fix plan mode docs (slash command not flag), fix modes page lin… #5117

Job	Run time
build-and-check	2m 36s
test-.agents	39s
test-npm-app	39s
test-cli	1m 8s
test-common	39s
test-packages/agent-runtime	57s
test-backend	38s
test-integration-sdk	54s
test-integration-packages/agent-runtime	38s
test-integration-packages/billing	39s
test-packages/internal	40s
test-integration-.agents	1m 7s
test-integration-common	42s
test-integration-packages/internal	42s
test-integration-backend	38s
test-web	44s
test-sdk	48s
test-integration-npm-app	40s
test-integration-cli	38s
test-packages/billing	43s
test-integration-web	34s
	17m 23s

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