Videos don’t appear in my iMac library

Since you have a timeline, you have a project. When you close the project it will automatically save to the project browser. If you don't see it there you may be looking in the wrong library or have not selected "All Projects" and the name of the library in the dropdown menu at the top of the project browser screen.

-- Rich

Go to the projects browser screen in the iMovie app. That's the screen that displays your projects as icons. Open the project and, if it displays without any missing media messages, then you are good to go. The project is in your iMovie library. To check, control-click on the iMovie library icon in the Movies folder (Finder menu/Go/Home/Movies) and then click on the Show Package Contents in the pop up menu. A screen will open that displays by name folders containing all of the projects and events in the library. Your project folder will be listed there. You can't play the project there, as that must be done through the iMovie app itself. Nor should you move, delete, or alter any files in the show package contents, or you risk corrupting your iMovie library.

-- Rich

The videos are in the iMovie Library not the Library on your iMac.