Describe the bug

When editing a custom provider in goose Desktop, the "Provider Type" dropdown always defaults to "OpenAI Compatible" regardless of the provider's actual engine type (Anthropic Compatible or Ollama Compatible). If the user saves any changes without manually re-selecting the correct provider type, the engine is overwritten to "openai", corrupting the provider configuration.

To Reproduce

1. Create a custom provider using CLI or Desktop with Anthropic Compatible or Ollama Compatible as the provider type
2. Go to Settings > Models > Configure providers
3. Click on the custom provider to edit it
4. Observe that "Provider Type" dropdown shows "OpenAI Compatible" instead of the actual type
5. Make any change (e.g., update display name) and click "Update Provider"
6. Check the provider's JSON config file in ~/.config/goose/custom_providers/ - the engine field is now "openai" instead of the original value

Expected behavior
The "Provider Type" dropdown should display the provider's actual engine type when editing, and saving changes should preserve the original engine unless the user explicitly changes it.

Screenshots
N/A

Please provide the following information

• OS & Arch: macOS
• Interface: UI (goose Desktop)
• Version: v1.15.0 and v1.16.0 (confirmed in both)
• Extensions enabled: N/A
• Provider & Model: Custom provider (Anthropic Compatible or Ollama Compatible)

Additional context
This is a data corruption bug. Users may unknowingly break their custom provider configurations by making unrelated edits. The issue appears to be in the Desktop UI's edit form not properly loading the existing engine value into the dropdown.