With that much data, even a simple Bayesian classifier should work pretty much perfectly.
They even mark their own Arts & Culture email as spam: https://x.com/MBanerjeePalmer/status/1962538753328664693
The only upside of having an actual mail server is the ability to say "this is incorrect, no one ever tried to send an email to this address/from this IP" or custom 55x messages.
You've functionally given yourself very little extra privacy because the vast majority of emails you send or receive will still cross through BigCorp servers (whether Google, Microsoft, Intuit, or other).
You can do the work to run your own mail server, but so few other people do that one end of the conversation is still almost always feeding a corporation's data lake.
No single BigCorp employee can go through all my mail.
If you're not convinced, no problem, please continue to enjoy your BigCorp email service.