Code snippet provided in documentation does not compile

[ign3u5]

Issue description

The documentation for compile-time logging source generation contains the following code snippet:

using System.Text.Json;
using Microsoft.Extensions.Logging;

ILogger<SampleObject> logger = LoggerFactory.Create(
    builder =>
    builder.AddJsonConsole(
        options =>
        options.JsonWriterOptions = new JsonWriterOptions()
        {
            Indented = true
        }))
    .CreateLogger<SampleObject>();

logger.CustomLogEvent(LogLevel.Information, "Liana", "Seattle");

public static partial class SampleObject
{
    [LoggerMessage(EventId = 23)]
    public static partial void CustomLogEvent(
        this ILogger logger, LogLevel logLevel,
        string name, string city);
}

This code does not compile due to it using a static class as a generic type argument. Even without this, no logs will appear in the console as the LoggerFactory is not properly disposed of and therefore the logs are not flushed.