AI Chat Web App template fails out-of-the-box on F5 in Visual Studio because of SQLite load error

### Description

On ARM64, the "AI Chat Web App" template throws a SQLite error immediately after creating a project inside Visual Studio when attempting to F5.

The app fails to load and throws:
Microsoft.Data.Sqlite.SqliteException: SQLite Error 1: 'The specified module could not be found.'

### Reproduction Steps

1. Install template pagacke via `dotnet new install Microsoft.Extensions.AI.Templates`
2. Create a new project using the "AI Chat Web App" template in Visual Studio with the following configuration:
- Framework: .NET 9.0
- AI service provider: GitHub Models
- Vector store: Local on-disk
- Leave the "Use Aspire orchestration" option unchecked.
3. Don't change anything in the code other than add the GitHub PAT
4. Press F5 (Debug) to run the template.
### Expected behavior

The app runs and no exception is thrown.

### Actual behavior

The app fails to load and throws:
Microsoft.Data.Sqlite.SqliteException: SQLite Error 1: 'The specified module could not be found.'

### Regression?

_No response_

### Known Workarounds

_No response_

### Configuration

_No response_

### Other information

_No response_