If you add appsettings.json to wwwroot folder and take a look at the network tab in browser's dev tools you will notice that Blazor WASM actually retrieves it at the start:

Retrieving appsettings
Figure 1. Appsetings.json is the second file retrieved by Blazor from the server after boot

That means it is possible to put another settings file that can be also shared with the server. Let's create a sharedsettings.json:

Shared settings file containing SharedSection with Shared Value
Figure 2. Sharedsettings.json content

To be able to merge it into appsettings.json during runtime we need to modify Program.cs like this:

public class Program
{
    public static async Task Main(string[] args)
    {
        var builder = WebAssemblyHostBuilder.CreateDefault(args);
        builder.RootComponents.Add("#app");

        var http = new HttpClient()
        {
            BaseAddress = new Uri(builder.HostEnvironment.BaseAddress)
        };

        builder.Services.AddScoped(sp => http);

        using var response = await http.GetAsync("sharedsettings.json");
        using var stream = await response.Content.ReadAsStreamAsync();

        builder.Configuration.AddJsonStream(stream);

        await builder.Build().RunAsync();
    }
}

To be sure that this worked let's modify Index.razor and display the setting:

@page "/"

@using Microsoft.Extensions.Configuration

@inject IConfiguration Configuration

<h1>Hello, world!</h1>

<p>Shared setting: @(Configuration.GetValue<string>("SharedSection"))</p>

Welcome to your new app.

<SurveyPrompt Title="How is Blazor working for you?" />

The effect is satisfactory 😁

Shared setting is visible in blazor app
Figure 3. Shared setting is visible in blazor app

Because Blazor WASM is hosted by ASP.NET core backend then after publishing the solution the wwwroot folder will be present in the main working path. A bit tricky thing is to add this shared json file to the server during debugging. That's why I decided to include it as a relative path to the file that is in the client project. I think the benefits justifies such a small inconvenience in the code. I modified my ASP.NET core Program.cs file like this:

public class Program
{
    public static void Main(string[] args)
    {
        CreateHostBuilder(args).Build().Run();
    }

    public static IHostBuilder CreateHostBuilder(string[] args) =>
        Host.CreateDefaultBuilder(args)
            .ConfigureAppConfiguration((_, config) =>
            {
                config.AddJsonFile("wwwroot/sharedsettings.json", optional: true, reloadOnChange: true); // When published

                var absoluteDebugSharedSettingsPath = System.IO.Path.GetFullPath("../Client/wwwroot/sharedsettings.json");
                config.AddJsonFile(absoluteDebugSharedSettingsPath, optional: true, reloadOnChange: true); // When debugging
            })
            .ConfigureWebHostDefaults(webBuilder =>
            {
                webBuilder.UseStartup();
            });
}

To check if that's working in backend as well I modified the WeatherForecastController.cs to look like this:

[ApiController]
[Route("[controller]")]
public class WeatherForecastController : ControllerBase
{
    private static readonly string[] Summaries = new[]
    {
        "Freezing", "Bracing", "Chilly", "Cool", "Mild", "Warm", "Balmy", "Hot", "Sweltering", "Scorching"
    };

    private readonly ILogger _logger;
    private readonly IConfiguration configuration;

    public WeatherForecastController(ILogger logger, IConfiguration configuration)
    {
        _logger = logger;
        this.configuration = configuration;
    }

    [HttpGet]
    public IEnumerable Get()
    {
        return new List
        {
            new WeatherForecast
            {
                Date = DateTime.Now,
                Summary = configuration.GetValue<string>("SharedSection"),
                TemperatureC = 22
            }
        };
    }
}

After compiling the weather forecast looks as expected 🎉

Weather forecast with value from sharedsettings.json
Figure 4. Weather forecast with value from sharedsettings.json

If you are having troubles following my steps then you can download example solution.