feat(agent): route slack-originated tasks to slack_app gateway product

[VojtechBartos]

Problem

The agent in the sandbox calls the LLM gateway as posthog_code regardless of how the task started. Slack-bot mentions are now billed differently from desktop tasks (gateway tags slack_app traffic with \$ai_billable=true), so the agent needs to send the correct product per task.

Changes

• Add "slack_app" to the GatewayProduct type union (packages/agent/src/utils/gateway.ts).
• Add "slack" to the Task.origin_product union (packages/agent/src/types.ts) to mirror the Python Task.OriginProduct.SLACK value already set on the backend.
• configureEnvironment now accepts originProduct?: Task["origin_product"] | null. Mapping: "slack" → slack_app, internal=true → background_agents, else → posthog_code. Call site reads preTask?.origin_product from the Task fetched at session init.
• Three new unit tests covering the slack → slack_app mapping, slack-over-internal precedence, and non-slack fallback.

Pairs with PostHog/posthog#59040 (gateway-side product registration + per-turn quota gate). Both ship behind the existing posthog-code-slack-availability flag — neither side has user-visible effect until the flag is enabled.

How did you test this?

I'm an agent. No manual testing.

• pnpm --filter @posthog/agent test src/server/agent-server.configure-environment.test.ts → 8 passed (5 pre-existing + 3 new).
• Typecheck error count unchanged from clean main (pre-existing module-resolution noise unrelated to this change).
• biome format --write clean on touched files.

Publish to changelog?

no