Closes #26949


## Summary

1. Split editor references to avoid borrow conflicts in event handlers
2. Check
[has_mouse_context_menu()](vscode-file://vscode-app/Applications/Visual%20Studio%20Code.app/Contents/Resources/app/out/vs/code/electron-browser/workbench/workbench.html)
state directly in tooltip conditional instead of caching stale value
3. Restructured context menu deployment to ensure proper sequencing:
hide popover → build menu → deploy menu → notify for re-render

**Screen recording**



https://github.com/user-attachments/assets/8a00f882-1c54-47b0-9211-4f28f8deb867



Release Notes:

- Fixed an issue where the context menu in the Git Blame view would be
frequently overlapped by the commit information tooltip.

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Co-authored-by: Finn Evers <finn.evers@outlook.de>