1. Does it happen when creating a new project using the map template?
2. Does it happen when creating a new project using the catalog template then inserting a map?
The locate pane is tied to the map, a locator needs to be added or loaded into the project in order to use the Locate pane. If the locators from the portal have not fully loaded in the project and the Locate pane was the last active window, the pane will not be available until the locators are loaded. In the Catalog pane under the Locators group you can see the locators that have been loaded and if you right-click the group there is an option to refresh the locators. I'm curious if you refresh the locators when you see the disabled Locate button behavior if that makes the button enabled instead of having to restart the ArcGIS Pro session.