## Why

BooCode's codecontext sidecar has 0% TypeScript type recovery — it cannot provide type signatures when the AI reads files. The `type-inject` project provides a published MCP server (`@nick-vi/type-inject-mcp`) that extracts TypeScript types, interfaces, function signatures from source files and injects them on file reads. Adding it to BooCode's MCP configuration directly solves the type blindness problem.

## What Changes

- Add `@nick-vi/type-inject-mcp` as an MCP server in BooCode's server config
- Add type-inject hooks for PostToolUse on Read (auto-inject types) and Write (type-check feedback)
- Add `lookup_type` and `list_types` tools available to agents
- Configure token budget and filtering options (onlyUsed, maxTokens, skipBarrelFiles)

## Capabilities

### New Capabilities
- `type-inject-mcp-server`: Register type-inject as MCP server in BooCode config
- `auto-type-injection`: Hook type signatures into file reads automatically
- `type-check-on-write`: Run type checker after file edits and report errors
- `type-lookup-tools`: Add `lookup_type` and `list_types` MCP tools for agents
