Fixes #1472 

<!-- CURSOR_SUMMARY -->
> [!NOTE]
> Switches `ProviderSettingSchema` union to `.passthrough()` variants to
accept extra fields and avoid overlapping schema conflicts.
> 
> - **Schemas**:
> - **`src/lib/schemas.ts`**: Update `ProviderSettingSchema` to use
`.passthrough()` on `AzureProviderSettingSchema`,
`VertexProviderSettingSchema`, and `RegularProviderSettingSchema` so
unknown fields are preserved and overlapping required fields don’t cause
mis-matches.
> 
> <sup>Written by [Cursor
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<!-- /CURSOR_SUMMARY -->