feat(litellm): improve reasoning model support and configuration UX

[balcsida]

Summary

Comprehensive improvements to the LiteLLM provider for better reasoning model support, variant-based reasoning effort control, and enriched model selection UX across CLI and desktop app.

Changes across 4 phases:

Phase 1: Reasoning parameter handling

• Strip false-positive reasoning parameters (reasoning_effort, thinking) using proxy model capabilities
• Only apply these params to models that actually support reasoning

Phase 2: Variant (reasoning effort) support

• Add variant field to ModelConfig for reasoning effort control (low/medium/high/max)
• CLI --variant flag and /variant slash command
• Map variant to reasoning_effort for reasoning-capable models

Phase 3: Enriched model info from proxy

• Fetch pricing and capability data from LiteLLM proxy's /model/info endpoint
• Display pricing in CLI configure dialog (e.g., "$3.00/$15.00 per 1M tokens")
• Add supports_reasoning to ModelInfo struct

Phase 4: Configuration UX improvements

• Show model capabilities (reasoning badge, pricing) in CLI and desktop model selectors
• Allow unlisted models for LiteLLM provider
• New /config/providers/{name}/model-info server endpoint returning enriched ModelInfo[]
• Desktop app: reasoning effort selector dropdown for reasoning models
• Desktop app: variant field flows through UpdateProviderRequest to ModelConfig

Type of Change

• Feature
• Bug fix
• Refactor / Code quality
• Performance improvement
• Documentation
• Tests
• Security fix
• Build / Release
• Other (specify below)

AI Assistance

• This PR was created or reviewed with AI assistance

Testing

• Unit tests for capabilities_to_model_info() including supports_reasoning field and sort order
• E2e test for openai::create_request + strip_reasoning_params interaction
• Live integration test for proxy model capabilities (requires running LiteLLM proxy)
• Manual testing: CLI configure dialog, desktop app model selection, reasoning effort selector, variant application to chat requests

Related Issues

Relates to #4221

Screenshots/Demos (for UX changes)

Desktop model selector now shows reasoning badges and pricing hints in the dropdown, with a "Reasoning Effort" selector appearing when a reasoning model is selected.