Loss of emails from hotmail account when transferring data to new Iphone 13 from old SE

Emails are not backed up, restored or transferred; they are downloaded from the email server after you add the account to the new phone. The same is true for contacts and calendars; for all of these the master copy is on the email provider’s server.

Log in to Hotmail on the web and see if the messages are visible in the webmail interface.

Transferring from one phone to another does not add or delete any email, it fact, it doesn’t touch email accounts at all, so that isn’t why the emails disappeared. If it happened around the same time that is a coincidence. Transferring doesn’t change anything on the phone that is the source; whatever was on it before the transfer is still on it after the transfer.