docs: add examples and docs for SSE support

[malcolm-kee]

Docs update and examples to clarify SSE support.

• how to configure OpenAPI spec so it can be detected by HeyAPI
• how to use the SSE-enabled functions for different clients. Common patterns for each clients are added, e.g. components examples added for Angular, Vue (Nuxt), and React (Next).
• add an example project

Partially resolves #2891

[changeset-bot]

⚠️ No Changeset found

Latest commit: c054b92

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[vercel]

@malcolm-kee is attempting to deploy a commit to the Hey API Team on Vercel.

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[pullfrog]

Reviewed the PR. Found one inaccuracy: the ofetch docs tip incorrectly claims native ofetch hooks apply to SSE connections. SSE uses raw fetch, so only Hey API interceptors apply. Left a comment with a suggested fix. The rest of the docs, example app, and spec are accurate and well-structured.

Task list (7/7 completed)

• Read the diff TOC and identify major areas of change
• Review docs changes (client docs + SDK plugin docs)
• Review the SSE example app (App.tsx, config, spec)
• Review generated client code in the example
• Review the OpenAPI spec for SSE
• Verify docs accuracy against actual generated code
• Self-critique and submit review

  ^{｜ [View workflow run](https://github.com/hey-api/openapi-ts/actions/runs/23598380028/job/68721227484) ｜ Triggered by [Pullfrog](https://pullfrog.com) ｜ [𝕏](https://x.com/pullfrogai)}

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 38.99%. Comparing base (51d56b3) to head (c054b92).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #3657   +/-   ##
=======================================
  Coverage   38.99%   38.99%           
=======================================
  Files         515      515           
  Lines       18901    18901           
  Branches     5591     5591           
=======================================
  Hits         7370     7370           
  Misses       9326     9326           
  Partials     2205     2205           

Flag	Coverage Δ
unittests	38.99% <ø> (ø)

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commit: c054b92

[pullfrog]

Low urgency. One inaccurate interceptor claim in the ofetch docs. The rest of the PR is solid — the docs, example, and spec are well-structured and consistent with the actual generated code.

  ^{｜ Fix all ➔ ｜ Fix 👍s ➔ ｜ View workflow run ｜ 𝕏}

[malcolm-kee]

@pullfrog check again.