Add action filter to [ApiController] annotated controller's actions only?

There's no built-in extensibility for the [ApiController] conventions that I know of, but you can achieve what you're looking for with the application model.

Here's an example implementation of an IControllerModelConvention that looks for the [ApiController] attribute, which you can fill in with your specific implementation:

public class ExampleControllerModelConvention : IControllerModelConvention
{
    public void Apply(ControllerModel controllerModel)
    {
        if (controllerModel.Attributes.OfType<ApiControllerAttribute>().Any())
        {
            // ...
        }
    }
}

You can register this convention in Startup.ConfigureServices or Program.cs for .NET 6+:

// Startup.ConfigureServices
services.AddControllers(options =>
{
    options.Conventions.Add(new SampleControllerModelConvention());
});

// Program.cs
builder.Services.AddControllers(options =>
{
    options.Conventions.Add(new SampleControllerModelConvention());
});

The IsApiController method in the ApiBehaviorApplicationModelProvider class you linked to handles the check a little differently:

private static bool IsApiController(ControllerModel controller)
{
    if (controller.Attributes.OfType<IApiBehaviorMetadata>().Any())
    {
        return true;
    }

    var controllerAssembly = controller.ControllerType.Assembly;
    var assemblyAttributes = controllerAssembly.GetCustomAttributes();
    return assemblyAttributes.OfType<IApiBehaviorMetadata>().Any();
}

This implementation supports the [ApiController] attribute being applied to the assembly the controller lives in. You likely don't need this if you're also using Views, but it's worth noting the difference in this approach.