upstreamable: Refactor built-in menu click handler in `menusToTemplate`

Currently, `menusToTemplate` re-attaches click handlers for built-in menu items by ID using a chain of `if/else if` statements. A better approach would be a map of ID -> handler, or a separate click handler registry that survives JSON serialization.

Related: #286

Search the repository for `menusToTemplate` and inspect how built-in menu click handlers are re-attached after JSON serialization. Review related issue #286 for context. The refactor is done when the existing built-in menu behavior is preserved without the current ID-based `if/else if` chain, using a maintainable handler map or registry.

Written by the indexing model from the issue text.