GlenB this is a fantastic question and has some nuance. But one of the areas where (we believe) our new approach is better than the prior one taken in classic Outlook.
If New Outlook's primary account is a paid Microsoft 365 personal or family account, is that different than New Outlook's primary account being an E3 or E5 account? From your response, I infer that they are identical - that New Outlook can be placed in premium mode with either a paid Personal/Family 365 account, OR with a paid BusStd/Prem/E3/E5 account, and it will then behave identically regardless of which license type is used to enable it.
The answer is that M365 Personal/Family and BusStd/Prem/E3/E5 have the same impact as the Primary account. The Outlook desktop client is now "paid for", so you can add whatever account you want.
Are the two license types identical in terms of New Outlook functionality they enable? If not, what differences are there?"
This is the important question. What features are available to you in the app are based on the license of the email syncing account you are in, not the Primary Account. That is there to validate you have paid for a desktop client. But if you have an E5 account with the security/IP/encryption, those will light up based on the E5 account. Regardless of if a consumer M365 Personal account is the primary. This was one of the main challenges we had with classic Outlook, when the licensing account determined the features regardless of the license/capabilities of the email syncing accounts. We'd have users accidentally change the licensing account to their personal accounts, and then lose a bunch of the capability for their work accounts. So the Primary Account in now there to act as your key to get in. But then the license of the email account itself controls what features you get. Put a different way, if you have E5 as your Primary and an Exchange Online Plan 1 user as a secondary, that secondary account doesn't get all the E5 security bells and whistles. They just get 'in' to Outlook for Windows. Which makes sense, since 99% of features these days are dependent on the mailbox and service itself. So if you underlying mailbox doesn't support tagging emails with confidential labels, having that button visible for an ExO P1 account doesn't make sense anyway.
One other follow up. I confirmed with the team that there should not be a toggle showing up in Outlook 2021 LTSC. If you have a repro of that, I'd love to follow up with you and investigate how that is going through. Definitely not an intended design.