Microsoft have released an extension for their Edge Browser which allows Outlook users to access their email without opening a dedicated tab in the browser.

They will also be “advertising” this extension in Outlook for Windows and Outlook on the web.

Microsoft Outlook Extension: https://microsoftedge.microsoft.com/addons/detail/microsoft-outlook/kkpalkknhlklpbflpcpkepmmbnmfailf

Microsoft 365 Roadmap: https://www.microsoft.com/en-gb/microsoft-365/roadmap?filters=&searchterms=82036

Edit: After "feedback" (complaints) from users Microsoft has backtracked and will no longer prompt the users to install the Edge extension in Outlook apps. They can still install it from the extension store.