settings_ui: Stop reading the clipboard on every frame (#56075) (cherry-pick to preview)

[zed-zippy]

Cherry-pick of #56075 to preview

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render_settings_item_link was calling cx.read_from_clipboard()
during render so it could show a check icon next to the copy-link button
when the matching link was on the clipboard. This had two problems:

• A clipboard read per visible setting per frame is too expensive.
• On Windows, reading the clipboard pumps the system message queue. If a
  queued message handler updates App while we're still rendering, GPUI
  panics with RefCell already borrowed (many occurrences observed).

Track the json_path of the most recently copied setting locally
instead. The check icon now reflects what was copied in this session via
this UI rather than whatever is on the system clipboard.

While this removes the most common offender, the underlying
gpui_windows reentrancy bug still exists: on_close /
on_request_frame callbacks can be invoked while App is already
borrowed on Windows, and can be triggered by any other
clipboard-touching code path. We should consider a follow-up PR that
handles this at the platform layer -- either by deferring callbacks that
re-borrow App, or by guarding individual handlers in
gpui_windows::events against reentrant borrow_mut calls.

Self-Review Checklist:

• I've reviewed my own diff for quality, security, and reliability
• Unsafe blocks (if any) have justifying comments
• The content is consistent with the UI/UX
  checklist
• Tests cover the new/changed behavior
• Performance impact has been considered and is acceptable

Release Notes:

• Fixed a crash on Windows that could occur when closing the settings
  window
• Improved the overall performance of the settings window