You can try to use this Nuget package In my project it logs Debug messages as well when correctly configured. It works always because using Console.WriteLine() See docs.

using Blazor.WebAssembly.Logging.Console;

...

builder.Logging.AddBrowserConsole()
    .SetMinimumLevel(LogLevel.Debug) //Setting LogLevel is optional
    .AddFilter("Microsoft", LogLevel.Information); //System logs can be filtered.

NOTE: in .NET 5 Blazor Web Assembly apps (NOT in Server side) if you use standard logging it will log to Browser console automatically. However it is possible your Browser is filtering out some logs. It means if you are not enabling "Verbose/Detailed" logging probably won't see Debug and Trace logs. Check your settings.

In Chrome it is here:

All above mentioned works only for Blazor Web Assembly (client side) Apps. If you want to log from a Blazor Server hosted app to your Browser console, then it is only possible with 3rd party tool. Use this Nuget package which will do the "magic". It works by sending logs from your server via SignalR channel to the user's Browser and logging to the console. Since it requires somewhat complex setup recommend to follow this detailed docs.

I've been able to add Serilog to my client application logging providers by adding the Serilog.Extensions.Logging NuGet package.

Then I used the following code:

using Serilog;
using Serilog.Core;
using Serilog.Extensions.Logging;

var builder = WebAssemblyHostBuilder.CreateDefault(args);

/* ... */

/* Serilog configuration
 * here I use BrowserHttp sink to send log entries to my Server app
 */
var levelSwitch = new LoggingLevelSwitch();
Log.Logger = new LoggerConfiguration()
    .MinimumLevel.ControlledBy(levelSwitch)
    .Enrich.WithProperty("InstanceId", Guid.NewGuid().ToString("n"))
    .WriteTo.BrowserHttp(endpointUrl: $"{builder.HostEnvironment.BaseAddress}ingest", controlLevelSwitch: levelSwitch)
    .CreateLogger();

/* this is used instead of .UseSerilog to add Serilog to providers */
builder.services.AddLogging(loggingBuilder => loggingBuilder.AddSerilog(dispose: true));