I know chrome has this as a separate feature, but I really think Edge can integrate this with the main omnibox (address bar). there can be an toggle added to settings to turn it off/on. if you look at the omnibox, it already is a combo-box, has lots of features, you can enable this flag to see it in action. edge://flags/#omnibox-suggestion-button-row
the description says: "Enable a button row on omnibox suggestions to present actionable items such as keyword search, tab-switch buttons, and Pedals. – Mac, Windows, Linux"
so to keep the UI clean and smart/useful, i think the best course of action is to integrate tab searching functionality into the Omnibox. one place to search for everything in Edge :)