How to use gmail api with service accounts or google Oauth in C# for sending mails?

Service accounts can only be used by the gmail api if you have a google workspace domain account.

You will need to set up domain wide delegation to a user on the Doman and the service account will then be able to send emails on its behalf. I guess creating a user called no-reply would be an option in this case.

Code is standard service account authorization code with the addition of adding gsuiteUser to delegate to.

        string ApplicationName = "Gmail API .NET Quickstart";
        const string serviceAccount = "XXXXX@XXXX-api.iam.gserviceaccount.com";

        var certificate = new X509Certificate2(@"c\XXXX-api-ed4859a67674.p12", "notasecret", X509KeyStorageFlags.Exportable);

        var gsuiteUser = "domainUser@XXXX.com";

        var serviceAccountCredentialInitializer = new ServiceAccountCredential.Initializer(serviceAccount)
        {
            User = gsuiteUser,
            Scopes = new[] { GmailService.Scope.Gmail }

        }.FromCertificate(certificate);

        var credential = new ServiceAccountCredential(serviceAccountCredentialInitializer);
        if (!credential.RequestAccessTokenAsync(CancellationToken.None).Result)
            throw new InvalidOperationException("Access token failed.");

        var service = new GmailService(new BaseClientService.Initializer()
        {
            HttpClientInitializer = credential,
            ApplicationName = ApplicationName,
        });

TBH forgot password functionality should be created on your webiste itself. I would assume that has its own domain and mail server. You should use that and not gmail api.