fix(providers): support authenticated LM Studio model discovery

[tsuckow]

Related GitHub Issue

Closes: #1392

Description

Adds support for providing an API Key for the LM Studio Provider, allowing using protected LM Studio servers

Also adds support for api/v1/models to retrieve the model list which was needed to test that the API key was working.

Adds a refresh models button which was used for testing connection issues

Test Procedure

Input for API Key

Working model picker

Hello world chat with authenticated provider

Pre-Submission Checklist

• Issue Linked: This PR is linked to an approved GitHub Issue (see "Related GitHub Issue" above).
• [?] Scope: My changes are focused on the linked issue (one major feature/fix per PR).
• Self-Review: I have performed a thorough self-review of my code.
• Testing: New and/or updated tests have been added to cover my changes (if applicable).
• [?] Visual Snapshot (UI changes only): If a user would notice this change at a glance (layout, theme tokens, brand elements, empty/error states), I've added or updated a *.visual.tsx snapshot in webview-ui/. See webview-ui/AGENTS.md → "When a UI change needs a snapshot".
• Documentation Impact: I have considered if my changes require documentation updates (see "Documentation Updates" section below).
• Contribution Guidelines: I have read and agree to the Contributor Guidelines.

Visual Snapshots

Additional Notes

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Get in Touch

Discord: drweldgood

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[codecov]

Codecov Report

❌ Patch coverage is 60.97561% with 32 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
...-ui/src/components/settings/providers/LMStudio.tsx	0.00%	23 Missing ⚠️
src/api/providers/fetchers/lmstudio.ts	86.84%	0 Missing and 5 partials ⚠️
src/core/webview/webviewMessageHandler.ts	87.50%	0 Missing and 2 partials ⚠️
src/api/providers/fetchers/modelCache.ts	0.00%	1 Missing ⚠️
...ew-ui/src/components/ui/hooks/useLmStudioModels.ts	50.00%	0 Missing and 1 partial ⚠️

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