I saw the solution to add the widget to that ini here: 4.23: How to auto-start Editor Utility Widgets? (new feature)
This wasn’t something that was clear or that I had an easy time googling/finding out, but it did help in having my widget start up when I open my project.
Right now, my plugin and widget work, but a user that downloads and activates my plugin will have to restart twice before that can all work. Maybe I’m just being nitpicky and I can just tell them that they’ll have to restart twice, or maybe tell them to edit the ini file before the first restart so they wouldn’t have to do it twice, but I just thought it would be nice if I could just avoid all that and make it so it just works after first restart