Just sign up to a new one if you dont use the old anymore. Plenty of free email services these days (gmail/outlook/protonmail/tutanota). And start using a password manager to remember stuff!
I meant included in website hosting not email. Many website hosting packages (not all) include basic SMTP so the website can send email and can setup forwarding/catch all rules for email addresses. The Tech guys will know all this though so yeah let them deal with it.
Just out of interest but can you setup forwarding for those accounts from the website hosting (if it includes SMTP) for those that have and use them actively? Theyd need to provide a forwarding address at least to send on to but at least theyd not lose access. Its all going to depend on the...