You’ll probably want to acquire some local IT help for maintenance and archiving, and for explaining.
Microsoft is moving to more modern connection authentication for their mail servers.
Apple and various other mail providers have also moved to more modern authentication for mail.
Here is the Microsoft statement:
https://support.microsoft.com/en-us/office/modern-authentication-methods-now-needed-to-continue-syncing-outlook-email-in-non-microsoft-email-apps-c5d65390-9676-4763-b41f-d7986499a90d
Basically, Microsoft are requiring better security for mail.
This authentication change will not disallow access from the Apple Mail app, nor from other recent mail clients.
To upgrade to the newer mail connection security, remove the Microsoft mail account from Apple Mail app, and re-add it.
This remove-and-add will not affect mail on the server, and will not affect mail stored on the client.
Per the linked Microsoft article: “Apple Mail supports Modern Authentication by default when you setup the account as Outlook.com”. Steps for migrating common mail clients re included, too.
If you want to migrate your mail to another mail provider or hosting provider, a tool such as imapsync can be useful for migrating mail to a different mail server, though simply downloading messages to a working mail client and then re-uploading to another mail server or archiving locally is probably the easiest and most common choice.
Paying for mail hosting is one way to get better support than is available from free services, if that is of interest. Free hosting services don’t have support. Not past the usually-limited value of scraping your data, that is.
I would most definitely and emphatically not suggest running your own mail server.
As for archiving your important data, that’s a whole ‘nother topic. And a large and ever-changing topic.
Here’s an older US Library of Congress government website with an intro to that topic: https://www.digitalpreservation.gov/personalarchiving/
Mail is not where I’d store any important information you want or need other folks to find, having assisted somebody with this. Wading through ads and spam and newsletters and the rest of the ephemeral detritus of life with email — looking for unknown nuggets or for important info — just isn’t going to happen, or it’s going to be rushed at best. (Not unless you’re a particularly notable person, or archiving your correspondence is legally required, that is.) As I’ve told more than a few folks running businesses and organizations, mail is where you bury your important organizational information. Mail is not where you preserve it.
More generally for Apple services, if you have not set up Recovery Contact and a Legacy Contact, go start there.
[been pondering whether to post some videos on these and related topics, but that’s all fodder for another discussion.]