I don't remember! Next Cloud is pretty sprawling with many optional modules and I don't remember all what they have enabled. I think you would not want anonymous people to edit a calendar because it would be too easy to vandalize. Although you know what you could do if you truely want publically editable would be to use something like Ethercalc (open source google sheets, there are many instances) or a google doc alternative (etherpad, cryptpad, or many others) and have a public document. They allow anon editing with rollbacks when needed. Do you actually need it to be a calendar? If not there are approx 10000 options.

If you want voting in a vaguely calendar-type format, you are looking for doodle or an alternative. Doodle is a tool to vote on meeting-type situations. I haven't used it in a few years. I wouldn't be surprised if it is now "enshitified" as the olds say. But there are various knock offs.

The Chatons website has a list of hosts, mainly for Framadate which is an open source doodle-type software. But you should open those drop down menus if that's not right because they know about a lot of stuff.

I wonder it this might be good for you: https://sondage.oisux.org/ it looks extremely minimal.