Thanks for your advices! I will surely read your source code. It is my first time when I create an extension and I think it would be great to make it crossbrowser.
Thank you for your ideas! I have a plan for adding the search and the ability to focus on the popup and I want to merge them together. I think that Alt+Shift+Y is not very helpful when you press it the first time, because it just selects the oldest of the visited tabs. And want it to focus on a special search item. Here is an image of what I want to do https://imgur.com/a/qlfVT0M. So, what do you think?
The Popup Tab Switcher is an attempt to bring the power of your system app switcher to a browser. The extension shows you a popup with last active tabs when you press its shortcut (Alt + Y by default). You cycle through them by holding Alt and pressing Y. By releasing the Alt key you switch to the chosen tab. This is like switching between apps in Windows (Alt + Tab) and in macOS (Cmd + Tab).
Also, when you close an active tab, you will be placed to the previously active one. It is more helpful than the default Chrome's behaviour, which activates the nearest tab.