The Chromium web browser and browsers based on it such as Google Chrome are not very flexible when it comes to placing extension icons in the interface.
Extension icons are always displayed in the main toolbar of the web browser. You can right-click those icons to hide them, or use drag and drop to change the position of icons on the toolbar.
What you cannot do is move them to another toolbar, or create a folder of sorts and move some of them inside.
Google resolves the "too many icons in the toolbar" issue by limiting the available space. You can resize the space by moving the mouse cursor on the end of the address form of Chromium and either move it to the left or right to increase or decrease the space that extensions have at their disposal.
The Chromium team is testing a new feature currently in the browser that looks very similar to how Mozilla handles icons in the Australis Hamburger menu.
It replaces the right arrow icon that users need to click on to display overflow tabs with a place in the Hamburger menu instead.
What this means is that all extension icons that do not fit on the main toolbar are displayed in the Hamburger menu instead.
Here is how this looks like
As you can see, space on the toolbar is reserved for a single extension only. The two other extensions that display icons in the toolbar have been moved to the menu instead from where they can be accessed.
You can use drag and drop to order extensions, for instance by dragging one of the extensions in the menu to the toolbar.
The feature is experimental which means that it is not clear if it will ever find its way into Chromium or Chrome natively. To use it right now, you will have to run Chromium with the --enable-extension-action-redesign parameter.
To do so on Windows, you would right-click the Chromium shortcut, select properties from the context menu, and add the paramter chrome-parameter to the target field. Make sure there is a space between chrome.exe and the parameter.
Restart Chromium and the feature is enabled in that version. It is likely that this is also working in Chrome Canary and Dev, or that it will be made available shortly.
To undo the change, delete the parameter from the target field again.