I have a ASP.NET Core 3.1 project like this sample: Sign-in a user with the Microsoft Identity Platform in a WPF Desktop application and call an ASP.NET Core Web API.
I'm using Identity web version 1.0 and Azure AD, single-tenant application.
I've edited the manifest adding appRoles since I'm requesting an application token only, and not a user token:
[... more json ...]
"appId": "<guid>",
"appRoles": [
    {
        "allowedMemberTypes": [
            "Application"
        ],
        "description": "Accesses the application.",
        "displayName": "access_as_application",
        "id": "<unique guid>",
        "isEnabled": true,
        "lang": null,
        "origin": "Application",
        "value": "access_as_application"
    }
],
"oauth2AllowUrlPathMatching": false,
[... more json ...]
I've also enabled the idtyp access token claim, to specify that this is an application token.:
[... more json ...]
"optionalClaims": {
    "idToken": [],
    "accessToken": [
        {
            "name": "idtyp",
            "source": null,
            "essential": false,
            "additionalProperties": []
        }
    ],
    "saml2Token": []
[... more json ...]
The following request is made with Postman. Please notice the use of /.default with the scope, which is mentioned in the documentation in relation to the client credentials grant flow.
POST /{tenant_id}/oauth2/v2.0/token HTTP/1.1
Host: login.microsoftonline.com
Content-Type: application/x-www-form-urlencoded
scope=api%3A%2F%2{client_id}%2F.default
&client_id={client_id}
&grant_type=client_credentials
&client_secret={secret_key}
The request returns an access_token which can be viewed with jwt.ms and looks like this, where actual data have been replaced by placeholders for security reasons.:
{
  "typ": "JWT",
  "alg": "RS256",
  "x5t": "[...]",
  "kid": "[...]"
}.{
  "aud": "api://<client_id>",
  "iss": "https://sts.windows.net/<tenant_id>/",
  "iat": 1601803439,
  "nbf": 1601803439,
  "exp": 1601807339,
  "aio": "[...]==",
  "appid": "<app id>",
  "appidacr": "1",
  "idp": "https://sts.windows.net/<tenant_id>/",
  "idtyp": "app",
  "oid": "<guid>",
  "rh": "[..].",
  "roles": [
    "access_as_application"
  ],
  "sub": "<guid>",
  "tid": "<guid>",
  "uti": "[...]",
  "ver": "1.0"
}
I notice that the token above does not include scp. This seem correct as this is an application token and not a user token. Instead it includes `”roles”´ as appropiate for an application token.
The access_token can now be used as bearer in a Postman Get:
GET /api/myapi
Host: https://localhost:5001
Authorization: Bearer {access_token}
The reponse to this request is 500 internal error. I.e. something is wrong. The access_token looks like a corrent application token, so the error seems to be on the ASP.NET Core 3.1 controller side.
The ASP.NET Core 3.1. project hosting the custom API, has a startup.cs which includes the following code:
services.AddMicrosoftIdentityWebApiAuthentication(Configuration);
// This is added for the sole purpose to highlight the origin of the exception.
services.Configure<JwtBearerOptions>(JwtBearerDefaults.AuthenticationScheme, options =>
{
    var existingOnTokenValidatedHandler = options.Events.OnTokenValidated;
    
    options.Events.OnTokenValidated = async context =>
    {
        if (context.Principal.Claims.All(x => x.Type != ClaimConstants.Scope)
            && context.Principal.Claims.All(y => y.Type != ClaimConstants.Scp)
            && context.Principal.Claims.All(y => y.Type != ClaimConstants.Roles))
        {
            // This where the exception originates from:
            throw new UnauthorizedAccessException("Neither scope or roles claim was found in the bearer token.");
        }
    };
});
The appsettings.json for the project includes:
"AzureAD": {
    "Instance": "https://login.microsoftonline.com/",
    "Domain": "mydomain.onmicrosoft.com",
    "ClientId": "<client_id>",
    "TenantId": "<tenant_id>",
    "Audience": "api://<client_id>"
},
... and the controller looks like this:
[Authorize]
[Route("api/[controller]")]
public class MyApiController : Controller
{
    [HttpGet]
    public async Task<string> Get()
    {
        return "Hello world!";
    }
}
The underlying cause of the 500 internal error is that this exception is thrown: IDW10201: Neither scope or roles claim was found in the bearer token. exception.
UPDATE:
(Please see the answer below for even more details).
This video on "Implementing Authorization in your Applications with Microsoft identity platform - june 2020" suggests that the missing piece is this flag JwtSecurityTokenHandler.DefaultMapInboundClaims = false; which need to be set in startup.cs - e.g:
public void ConfigureServices(IServiceCollection services)
{
    // By default, the claims mapping will map clain names in the old format to accommodate older SAML applications.
    //'http://schemas.microsodt.com/ws/2008/06/identity/clains/role' instead of 'roles'
    // This flag ensures that the ClaimsIdentity claims collection will be build from the claims in the token
    JwtSecurityTokenHandler.DefaultMapInboundClaims = false;
    
    [...more code...]