Require anonymous submissions to be approved

you need to uncheck user capability publish_events under Events > Settings > General > User Capabilities

When I do that, it makes the form inaccessible. I want anonymous submissions, but I want them to require approval before publishing.

Do you have publish_events, publish_recurring_events and publish_locations all unchecked on the user capabilities page?

Do you also have “Allow anonymous event submissions” set to Yes under Events > Settings > General > Event Submission Forms?

This may help:
https://wp-events-plugin.com/documentation/user-event-guest-submissions/

Okay, if I uncheck publish_events and uncheck publish_recurring_events but leave publish_locations it works.