Use plural plugin install extension in core

[zswang-oai]

Why

With the extension and core backend in place, core can expose the plural tool while preserving Noah's original install picker behavior.

What changed

• register request_plugin_installs through the extension executor
• use the single-entry mode for TUI and the plural mode for desktop clients
• route recommendation context and list-tool guidance to the plural name
• read nested picker metadata for elicitation telemetry
• stop compiling the old core handler
• update integration coverage for the plural tool

The emitted picker metadata remains the original nested entries / categories contract, including per-entry Install buttons and the Skip / Continue footer.

Stack

This is PR 6 of 7.

• Base: Add plugin install extension backend #28818
• Next: Remove singular plugin install tool #28820

[chatgpt-codex-connector]

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[chatgpt-codex-connector]

Reserve the core plugin installer before extension tools

When a session has an extension contributor that registers a plain request_plugin_installs tool, this appends the core installer after contributed extension tools. append_extension_tool_executors keeps the first executor for a tool name and skips later duplicates, so in that scenario the model-visible install suggestion tool is backed by the external extension instead of CoreRequestPluginInstallsBackend, and plugin recommendations/list results can no longer trigger the expected Codex install elicitation.

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