feat: add support lmstudio api

[Happyfunnysad]

Before Submitting This PR

• I have searched existing issues and pull requests (including closed ones) to ensure this isn't a duplicate
• I have read CONTRIBUTING.md

Human Written Description

Add support for the LMStudio API (OpenAI-like API) in Handy post-processing. This makes LM Studio available as a separate provider instead of relying on the generic Custom provider configuration.

Testing

• Queried the LM Studio OpenAI-compatible /v1/models endpoint successfully against the provided test host.
• Confirmed available model IDs were returned from LM Studio.
• Ran Windows x64 GitHub Actions build successfully: https://github.com/Happyfunnysad/Handy/actions/runs/30020663799
• Downloaded CI artifacts locally:
  • Handy_0.9.4_x64_en-US.msi
  • Handy_0.9.4_x64-setup.exe

Note: the CI artifact build is unsigned.

Screenshots/Videos

AI Assistance

• No AI was used in this PR
• AI was used (please describe below)

If AI was used:

• Tools used: OpenAI Codex
• How extensively: AI-assisted codebase exploration, implementation, CI workflow adjustment, LM Studio endpoint testing, and Windows x64 CI build verification.