Cannot set up a Mail account in Ventura nor migrate mail from Catalina

Thanks - read that but it makes things too simple, by assuming that you can log in in the first place.

When I get to 'set up account' I fill in the boxes exactly the same as they are on the Catalina Mac - user name, e-mail address, password. Then I get the spinning icon and after five minutes or so: 'unable to authenticate user name or password'. This is by using the same details exactly that are already on my Mail account in the older computer. I've tried migrating Mail but the only option is to migrate ALL the applications, I can't select simply Mail alone. I've linked both iMacs by Bluetooth, by broadband and by physical ethernet cable but the newer Ventura machine won't do anything. It's connected to the Internet - I'm on forums like this using Safari and it links to my iPhone - but it won't seemingly talk to the older iMac. Are there permissions or something that I haven't ticked?

No, at this point the new Ventura machine is going on the shelf where it can gather dust. I'll reload everything on the Catalina Mac and go back to using that, and remember for the future.

Apple Support will tell me to contact my e-mail provider; my e-mail provider tells me to contact Apple. It just goes round in circles. I can't create any kind of account, it just tells me it identifies both incoming mail server and outgoing as IMAP, it fills in my details automatically, then tells me it can't 'verify account name or password'.

Ok - can't edit that last reply so update as of six hours later - still nothing. I'm connected to the Internet via BT, surfing Safari, and accessing my emails online, but no emails will download to my Ventura Mac. I cannot add a Mail account by any means. I even migrated all applications from the older Mac, still no go. All I get is the initial dialog box - add user name, e-mail and password... then a red message that it's not recognised. I can't even get to a stage of checking ports or other solutions - I just cannot even set up an initial account. How can one Mac work on user name and password that has been in use since 2018, and a newer one, not, with the same details added?