When I fired up the "Windows" app on my Windows 11 laptop the first thing it asked was for me to sign in. You are correct that this is not the case for iOS (I have no personal experience with Android or Mac).
What's confusing all of us is they have so many things with similar names. Check out these posts:
https://techcommunit...windows/4390893
https://techcommunit...support/4397724
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Relevant parts:
This blog applies only to the Windows App replacement of the Remote Desktop app downloaded from the Microsoft Store. It does not apply to the Remote Desktop client standalone installer (MSI), which can be downloaded from Download and install the Remote Desktop client for Windows (MSI).
Remote desktop users: Users connecting to remote desktops from the Remote Desktop app should use Remote Desktop Connection until support for this connection type is available in Windows App.
What's not changing
Remote Desktop Connection (Microsoft Terminal Services Client, MSTSC) will remain a supported application for connections to remote desktops.
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So it looks like the app you found will continue to be supported. And at some point they will update the "Windows" app for Windows.
Whatever the case I'm confident that Microsoft would not prevent you from accessing Remote Desktop from their own OS. Especially when they just updated it for every other platform.