docs: clarify runtime mode guidance across deploy guides

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Stack for rivet-dev/rivet

• #5482 feat(frontend): sync compute connect dialog with onboarding …
• #5477 docs: use RIVET_POOL instead of the unread RIVET_RUNNER env …
• #5479 docs: clarify runtime mode guidance across deploy guides 👈
• #5476 feat(frontend): default onboarding to runner mode and make c …
• #5478 refactor(frontend): rename serverfull to serverful
• main

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_{change upwztvmx}

[claude]

Review

Docs-only PR that clarifies runtime mode terminology (Runner as default vs. Serverless) and fixes deploy guides that previously described Runner-mode deployments (Kubernetes, Railway, VM/bare-metal) as if they needed inbound public URLs and WebSocket idle-timeout tuning. I verified the technical claims against the current codebase:

• RIVETKIT_RUNTIME_MODE defaulting to "envoy" (Runner) when unset, and the "envoy" | "serverless" type, confirmed in rivetkit-typescript/packages/rivetkit/src/utils/env-vars.ts:52-61.
• RIVET_POOL as the current pool-assignment env var (replacing the old RIVET_RUNNER), with envoy.poolName defaulting from getRivetPool(), confirmed in env-vars.ts:18 and registry/config/envoy.ts:13.
• registry.start() selecting Runner mode by default and switching to a bound HTTP listener under RIVETKIT_RUNTIME_MODE=serverless, confirmed in registry/index.ts.
• The #runner/#runners anchor rename (heading changed from "Runners" to "Runner"): confirmed no other tracked file in the repo still links to the stale #runners anchor.
• The Railway "App Sleeping" warning replacing the old "enable sleeping to save costs" tip is a real correction: sleeping suspends the process and drops its outbound connection to Rivet, and Railway only wakes on inbound HTTP, so a sleeping Runner would never reconnect. Good catch.
• The dashboard "Runners" tab label referenced in the Kubernetes/Railway/VM verify steps matches the actual frontend UI (frontend/src/routes/.../tokens.tsx).

Finding: stale canonical env var reference is now more visibly inconsistent. website/src/content/docs/general/environment-variables.mdx (not touched by this PR) still documents RIVET_RUNNER as "Runner name (default: default)" under "Runner Configuration", and does not mention RIVET_POOL at all. Grepping the codebase, RIVET_RUNNER (exact) is not read anywhere in current TS or Rust code; it looks like a leftover from before the pool env var was renamed to RIVET_POOL. Since this PR newly emphasizes RIVET_POOL in runtime-modes.mdx ("Use RIVET_POOL to assign runners to a pool"), a reader who then checks the canonical "all environment variables" page will find a different, non-functional variable name for the same concept. Not a regression introduced by this PR, but worth fixing in the same change or a fast follow, since this PR is specifically about clarifying runtime-mode env var guidance.

Nit: the tokens.tsx anchor fix (#runners to #runner) is a one-line, easy-to-miss change bundled into an otherwise pure-docs PR. Worth calling out explicitly in the PR description since it is the only frontend file touched.

Overall this is an accurate, well-verified documentation improvement. No bugs, security, or test-coverage concerns since this is a content-only change, and no <CodeSnippet> blocks were added or modified, so there is no snippet type-check risk from this change.