feat: add copy to clipboard button to plan mode

[MattPua]

Adds a copy-to-clipboard button to the plan view.

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Created with PostHog Code

[trunk-io]

😎 Merged manually by @MattPua - details.

[github-actions]

React Doctor found no issues in the changed files. 🎉

_{Reviewed by React Doctor for commit 39d6aac.}

[greptile-apps]

_{Reviews (1): Last reviewed commit: "feat(permissions): add copy-to-clipboard..." | Re-trigger Greptile}

[github-actions]

Purely additive UI change — adds a copy-to-clipboard button. The bot's clipboard-Promise concern was resolved with async/await and try/catch. The remaining setTimeout without unmount cleanup is a cosmetic pattern issue, not a production risk.