Squarespace is a bit different that some other builders. For many of the pages, saving your changes also publishes your changes. With collection pages like Events, Shop, and Blog things are a little different.
The next time you click on those three dots next to an event and select settings, click "Options" rather than "Content" in the panel that pops up. Once the options panel appears, click on "Status" and you will have the option of setting the status of that particular event as a "Draft" "Needs Review", "Published", or "Scheduled". After selecting one of these (and setting a date and time if you selected Published), click "Save" at the top left of the options panel.