feat(core): add integration-backed search

[nexxeln]

Summary

• add a Location-scoped Search module backed by Integration capabilities and durable provider selection
• migrate Exa and Parallel out of the websearch tool into first-party integration plugins
• onboard provider choice inline and support changing/authenticating the default from the TUI connection dialog
• regenerate V2 clients and add the integration capability selection migration

Testing

• bun turbo typecheck
• focused Core Search, Integration, Form, plugin, and websearch tests
• Schema, Protocol, Client, SDK, and TUI package tests/typechecks

Part 1 of #35038.