Docs: make getting started example open-safe

[nerdchanii]

Summary

• disable the getting-started send button until the example WebSocket connection opens
• reset the send state when the connection closes or the example unmounts
• keep the example structure otherwise unchanged

Context

• follow-up to the post-merge Codex review comment on Docs: rewrite the public home and getting-started flow #122

Verification

• npm run docs:build
• npm run lint

[nerdchanii]

@codex review

Context:

• Follow-up to the missed post-merge review comment from Docs: rewrite the public home and getting-started flow #122
• Scope: only make the public getting-started example safe before the socket opens

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. You're on a roll.

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[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. What shall we delve into next?

ℹ️ About Codex in GitHub

Your team has set up Codex to review pull requests in this repo. Reviews are triggered when you

• Open a pull request for review
• Mark a draft as ready
• Comment "@codex review".

If Codex has suggestions, it will comment; otherwise it will react with 👍.

Codex can also answer questions or update the PR. Try commenting "@codex address that feedback".