Подключите SecretClient к проксиму

using Azure.Extensions.AspNetCore.Configuration.Secrets; // v1.2.1
using Azure.Identity; // v1.5.0
using Azure.Security.KeyVault.Secrets; // v4.3.0-beta.4

var builder = WebApplication.CreateBuilder(args);

var webProxy = new WebProxy(new Uri("{proxy_url}")) { 
    Credentials = CredentialCache.DefaultNetworkCredentials 
};

var httpClient = new HttpClient(new HttpClientHandler { 
    Proxy = kpmgWebProxy, SslProtocols = SslProtocols.Tls12 | SslProtocols.Tls11 | SslProtocols.Tls 
});

var secretClientOptions = new SecretClientOptions { 
    Transport = new HttpClientTransport(httpClient) 
}; 

// `Azure.Security.KeyVault.Secrets` package version < 4.3.0 does not have the tenant discovery feature, therefore you will have to set this i nthe options. 
/*var defaultAzureCredentialOptions = new DefaultAzureCredentialOptions()
{
    VisualStudioTenantId = "",
};*/

var secretClient = new SecretClient(
    new Uri(azureKeyVaultUrl), 
    new DefaultAzureCredential(/*defaultAzureCredentialOptions*/), 
    secretClientOptions);

builder.Configuration
    .AddAzureKeyVault(secretClient, new KeyVaultSecretManager());

var output = builder.Configuration
    .GetSection("ApplicationInsights:InstrumentationKey").Value;
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