FE-1500: add the example embed route

[kube]

🌟 What is the purpose of this PR?

Adds the embed route /embed/examples/<slug>, rendering the regular Petrinaut component read-only with embed options. This makes the embed URL contract available for oEmbed immediately; a compact preview surface replaces the component in a later PR without changing the contract. Stacked on #9362.

🔗 Related links

• FE-1500

🔍 What does this change?

• New embed route; direct browser visits render it too, so the view can be tested without an iframe harness. Framing policy is enforced by HTTP headers (vercel.json, in the oEmbed PR), not by client-side checks. Query params outside the contract are inert rather than redirected away: validateSearch drops them, and rewriting the address bar would need a document reload, which an embed must avoid.
• EmbeddedExamplePage lazy-loads a read-only Petrinaut with all net-management controls hidden and a plain title in the top bar; navigation always uses replace-history inside the iframe. (The review presentation profile that hides authoring controls arrives later in the stack, in FE-1500: add editor presentation profiles #9425.)
• Embed URLs carry the same shared scenario/subnet/selection contract as the canonical page (FE-1500: add versioned examples and read-only pages #9362), so there is no embed-specific codec.
• The page reuses useSharedSearchNavigation from FE-1500: add versioned examples and read-only pages #9362 with a replace-only history policy, so the embed never grows the host page's history; controls that drive URL-unrepresentable state (the mode switcher, the viewport-settings overlay) work inside the embed instead of silently snapping back.
• Adds the /embed/examples/* SPA rewrite to vercel.json.

Pre-Merge Checklist 🚀

🚢 Has this modified a publishable library?

This PR:

• does not modify any publishable blocks or libraries, or modifications do not need publishing

📜 Does this require a change to the docs?

The changes in this PR:

• are internal and do not require a docs change

🕸️ Does this require a change to the Turbo Graph?

The changes in this PR:

• do not affect the execution graph

🐾 Next steps

• A compact PetrinautPreview surface replaces the full component inside the embed later in this stack, keeping the URL contract property-tested identical.

🛡 What tests cover this?

• Existing: the contract's own unit and fast-check suites in FE-1500: add versioned examples and read-only pages #9362 cover the search handling this route relies on; -index.test.tsx-style route coverage is not duplicated here.

❓ How to test this?

1. Checkout the branch and run yarn workspace @hashintel/petrinaut build:lib, then yarn workspace @apps/petrinaut-website dev.
2. Visit http://localhost:5173/embed/examples/gases-1-pn directly and confirm the read-only embed renders.
3. Confirm scenario, subnet, and selection changes rewrite the URL without adding history entries, and that a query param outside the contract (for example ?mode=simulate) is ignored.

[vercel]

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Project	Deployment	Actions	Updated (UTC)
hash	Ready	Preview	Aug 31, 2026 2:50pm
petrinaut	Ready	Preview	Aug 31, 2026 2:50pm
petrinaut-docs	Ready	Preview	Aug 31, 2026 2:50pm

1 Skipped Deployment

Project	Deployment	Actions	Updated (UTC)
hashdotdesign-tokens	Ignored	Preview	Aug 31, 2026 2:50pm

[semgrep-code-hashintel]

Semgrep found 1 regex_dos finding:

• apps/petrinaut-website/src/main/app/brunch-demo/brunch-endpoint.ts
  • L8-18 - Triage

Ensure that the regex used to compare with user supplied input is safe from regular expression denial of service.

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