[FEATURE] Support project-local TypeScript SDK in typescript-lsp plugin

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

The typescript-lsp plugin currently uses the system-installed typescript-language-server without allowing configuration of initializationOptions.tsserver.path. This means Claude Code always uses the global TypeScript version rather than the project's local TypeScript.

Proposed Solution

Allow LSP plugin configurations to specify initializationOptions, enabling users to set:
```json
{
"initializationOptions": {
"tsserver": {
"path": "./node_modules/typescript/lib"
}
}
}

  Or automatically detect and use ./node_modules/typescript when present in the project root.

### Alternative Solutions

_No response_

### Priority

Medium - Would be very helpful

### Feature Category

Other

### Use Case Example

  - Projects pinned to specific TypeScript versions for compatibility reasons
  - Large codebases where TypeScript version affects type inference behavior
  - Ensuring LSP diagnostics match actual build output

### Additional Context

_No response_