Migration Assistant and Mail

Hi there. I got a new iMac today - it's brilliant, but transferring my email is driving me nuts.

New iMac is running latest version of Big Sur.

My old MacBook Air is running El Capitan (that's as far as it will go)

I've run Migration Assistant twice - all my data files transfer, but each time my email accounts don't transfer. On the Air I use the Apple Mail app to coordinate 5 Gmail accounts (personal and work). As part of that, I have a very detailed mailbox structure under "On My Mac", so those emails are all stored on my hard drive, and backed up via Time Machine.

After Migration, when I open Mail on the iMac there is nothing inside -no accounts transferred, and no emails. I've spoken to Apple support twice and they think they should have migrated ...

I tried just adding my main work account to Mail on the iMac, logging in as a new account. It did at least connect, but it downloaded 7 years of history - 7000 emails - all in one Archive Folder. Useless to me.

One concern I have is that I can't even see an 'On My Mac' option in Mail on the iMac.

All I can think of doing is exporting the folders on my Air, moving them via the cloud, and then importing them on the iMac, but this feels clunky. Should there be a more automated way of doing it?

I'm also wondering if, because MA seems to have transferred everything else, if the mailboxes are actually sitting on my iMac, but Mail can't see/use them??

I love Apple stuff but things like this drive me nuts ...

Thanks