This should be normal in a fresh install.
The menu option plugins > manage and install plugins will let you add plugins. I don't think there's a toolbar button for that.
Bear in mind that not all plugins install an icon to the plugins toolbar - they may appear elsewhere.
- in the plugin / vector / database / web menu
- in their own menu
- in processing toolbox
- in their own toolbar
- in a panel (dock)
Generally, the newer plugins tend to have their own toolbar.
After a while it's easy to get a lot of toolbar clutter. Right-click on some empty space on any toolbar and you'll get a menu which lets you see which toolbars are enabled and turn them on or off.