Ok, well I called Apple support again on Friday on this time got a senior advisor who actually understood what I was trying to do and what wasn’t working. He escalated the issue as adding a second account is clearly something that was supported up until the newest iOS/iPadOS and is no longer working.
But…he DID provide a workaround that got it working for me.
When you go to set up the secondary iCloud account in the Mail settings, choose “Other” instead of the iCloud option. You’ll need to set up the mail servers manually.
instructions here:
https://support.apple.com/en-us/HT201320
Make sure you choose IMAP.
Mail servers for iCloud,
incoming mail server: imap.mail.me.com
outgoing mail server: smtp.mail.me.com
For both, you’ll input the server addresses in the ‘Host Name’ field for each.
Under username for each mail server, enter your iCloud name without the ‘@icloud.com’.
Now, here’s the trick, under ‘Password’, entering you iCloud password here WILL NOT WORK. You need to create an App Specific password under setting in you AppleID.
Use a web browser and log into you secondary account’s AppleID. (AppleID.Apple.com)
Under settings there, create an App Specific password. It will auto generate. Make sure you copy this password somewhere as once you leave the screen you won’t be able to see it again.
Now, once you have that new App Specific password, go back to Mail settings and use the App specific password for both the incoming and outgoing mail servers.
And that should do it. Worked for me.
The support agent escalated this issue to engineering and I have a case I can check to see if it’s been updated with a resolution. Hopefully, Apple fixes this bug in an upcoming iOS update and we won’t have to jump through hoops to add a second iCloud account in Mail after that.