The error messages seems clear: The SMTP server requires authentication and it seems you didn't configured that in your database mail setting. I suggest that you talk to your SMTP people about the mail config to get the configuration for the mail profile right.
How to configure SMTP for sql managed Instance
Message
The mail could not be sent to the recipients because of the mail server failure. (Sending Mail using Account 3 (2021-02-16T08:00:07). Exception Message:
1) Exception Information
Exception Type: Microsoft.SqlServer.Management.SqlIMail.MailFramework.Exceptions.BaseMailFrameworkException
Message: Cannot send mails to mail server. (Transaction failed. The server response was: 5.7.1 Authentication required)
Data: System.Collections.ListDictionaryInternal
TargetSite: Void Send(Microsoft.SqlServer.Management.SqlIMail.MailFramework.Framework.IMessage)
HelpLink: NULL
Source: DatabaseMailProtocols
HResult: -2146232832
StackTrace Information
at Microsoft.SqlServer.Management.SqlIMail.MailFramework.Smtp.SmtpMailSender.Send(IMessage msg)
at Microsoft.SqlServer.Management.SqlIMail.Server.Controller.ProfileMailSender.SendMailToAccount(Account a, IMessageSender ms, OutMailItem si)
2) Exception Information
Exception Type: System.Net.Mail.SmtpException
StatusCode: TransactionFailed
Message: Transaction failed. The server response was: 5.7.1 Authentication required
Data: System.Collections.ListDictionaryInternal
TargetSite: Boolean CheckResponse(System.Net.Mail.SmtpStatusCode, System.String)
HelpLink: NULL
Source: System
HResult: -2146233088
StackTrace Information
at System.Net.Mail.RecipientCommand.CheckResponse(SmtpStatusCode statusCode, String response)
at System.Net.Mail.SmtpTransport.SendMail(MailAddress sender, MailAddressCollection recipients, String deliveryNotify, Boolean allowUnicode, SmtpFailedRecipientException& exception)
at System.Net.Mail.SmtpClient.Send(MailMessage message)
at Microsoft.SqlServer.Management.SqlIMail.MailFramework.Smtp.SmtpMailSender.Send(IMessage msg).
)