ArtTray

Minimizing a window automatically sends it to the taskbar, but some applications in particular are configured to go directly to the tray area. There’s not really a default method to enable this on all windows, but applications like ArtTray are specially designed just for this purpose so the taskbar stays clean.

Lightweight and easy to use

Although the application is designed to target almost any kind of window, it doesn’t need to make any changes to system registries in order to function, neither does it require an installation. This means you can carry it around on a thumb drive to use on other computers besides your own, while the target PC’s health status remains intact.
The application itself goes to the tray area on launch, and there’s no tooltip to let you know it’s there. However, interacting with it is only necessary if you want to close it, because there are no options to configure, or related windows or interfaces of any kind.

Minimize everything except File Explorer

The core function here is to hide any minimized window to the tray area, and this is done directly from the minimize function found in the title bar, with no additional content added. This means that you’re not able to minimize anything to the taskbar as long as the application is running, except for Explorer instances, which are not affected by this feature.
On the bright side, every minimized window shows its dedicated icon in the tray area to make identification easy. Bringing a window back up is simply done by interacting with the tray icon. If you want to make it run with Windows, you need to manually add a shortcut to the Startup folder, because there’s no such built-in option.

To end with

Bottom line is that even if windows aren’t all visible on the desktop, bundling them together in the taskbar still isn’t a solution. Luckily, ArtTray can target any kind of window which doesn’t belong to File Explorer, fitting it with its own icon for easy identification, and doesn’t even require installation to run.