LSP support

### Feature summary

Consider adding support for LSPs

### What problem are you trying to solve?

Honestly surprised this wasn't mentioned yet, but it would be _really_ great to get LSP support for this app. The CLI has it already: https://docs.github.com/en/copilot/concepts/agents/copilot-cli/lsp-servers

### Proposed solution

_No response_

### Workflow impact

_No response_

### Installation context

_No response_

### Additional context

_No response_

Start by reviewing the app's architecture and the linked Copilot CLI LSP documentation to determine where language-server support would belong. The issue provides no files, entry points, workflow, or acceptance criteria, so define the integration scope and a verifiable completion condition before implementation.

Written by the indexing model from the issue text.