There's actually two different AI settings to turn off for Gmail. There are the settings that are under 'Google Workplace Smart features', and there's an additional one above it just called 'Smart Features'.
Turning off the settings under the 'Google Workplace Smart Features' doesn't seem to affect your inbox. But if you turn off that top 'Smart Features' option, you can no longer use the different inbox categories that Gmail would default sort emails to.
With Smart Features enabled:
With Smart Features Disabled:
It's really shitty that they've tied those inbox categories into the AI stuff. I turned Smart Features off, and now my phone is being inundated with notifications for a lot of the emails that would have gone in those categories. Previously, I would only get notifications for emails that end up in the main inbox when my notification settings were set to 'All'.
There is a way to create your own sorting labels (like the one I'd been using for Dracula Daily in the screenshot above), but they don't quite work the same way as the inbox categories. If you create a label, you'll be able to view only the emails you set to be categorized underneath it, but those emails will still show up underneath the main inbox, too.
Say you create a new 'Social' label for social media notifications to replace the Social category Inbox. If you click the 'Social' label, you would see all the emails that are filtered to go there, in addition to those same emails showing up in the main inbox. With the inbox categories enabled (and now AI features too), you would only see social emails in the Social inbox, and they would not show up under the main inbox, nor would you get notifications for them by default.
If you do want to go the label route and create your own, here's a link on how to do so. It can be done using a computer or through the Apple apps, but it won't work in the Android app (which makes zero sense to me).
There might be a way to play with the app notification settings so they're more filtered, but from what I see initially, it's not promising.
If you were relying on 'Important First' sorting for your inbox or 'High Priority Only' for notification settings, those are disabled when the AI feature is disabled as well.
(I can edit this later to add alt ids to the images when I'm not on my phone)