Hi @Todd Osborn ,
Sounds like an expected behavior as based on what I am aware of, the New Outlook is built on the basis of Outlook on the Web. So it makes senses that disabling Outlook on the Web will also affect the New Outlook client.
Given this, I'd recommend switching the toggle off in the new Outlook to going back to the classic version, as the classic Outlook is controlled separately.
Meanwhile, you can consider disabling users' access to the New Outlook by following the document below:
Enable or disable employee access to the new Outlook for Windows
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