Old code:

 new ServiceClient( instanceUrl: uri, tokenProviderFunction: GetToken, useUniqueInstance: true, logger: logger);

Result: a bunch of log messages, but no warnings.

Switching to the new constructor:

 new ServiceClient(connectionOptions: new() { AccessTokenProviderFunctionAsync = GetToken, AuthenticationType = Microsoft.PowerPlatform.Dataverse.Client.AuthenticationType.ExternalTokenManagement, ServiceUri = uri, Logger = logger, });

Result: warning Client ID not supplied, using SDK Sample Client ID for this connection logged each time.

edit: My understanding is that a client ID is not required when providing an access token directly. Setting the client ID property to null, "", or a value doesn't seem to have any effect.