You’ll want to describe more of your configuration; your local system and its operating system and the remote system and its operating system, as a start. Or might want to check with your local IT folks, if you have those around.
Apple Remote Desktop is a quite different product from Microsoft Remote Desktop.
Apple Remote Desktop runs only on macOS, and is usually used to access and remotely manage numbers of Macs. It;s a Mac screen-sharing package, with the ability to push software updates and to manage and make other changes to other Macs.
There are versions of Microsoft Remote Desktop for various platforms, including for macOS.
If you’re having issues with and are running the Microsoft Remote Desktop app here on macOS (or are running that else-platform, for that matter) and are not running the Apple Remote Desktop app on macOS, then make sure the Microsoft product is patched to current, and then check with the Microsoft Support folks.
The Microsoft Remote Desktop app probably isn’t particularly tied to the bash shell change. The Microsoft product is usually used to access Microsoft Windows and Windows Server systems—and not typically with Apple systems—which means the target system will not be macOS and will not be getting a bash-to-zsh diagnostic.
If you’re using a Microsoft Windows system locally and are accessing macOS remotely, then you may be running into the message after a macOS upgrade. What effect that will have here is largely up to the app vendor, or to whoever wrote the shell script that’s apparently being invoked here somehow.
The zsh diagnostic message itself is benign. The diagnostic can be suppressed using the setting mentioned in the previously-linked thread. Somebody will want to look into the shell scripts being used on macOS, though. Those may well suddenly stop working after some future macOS upgrade, and may or will then require some changes in the configuration or within the app(s) involved.