When you create in your user profile a application token, you can then click on the created token and get a " Credentials for ..." window, where multiple login commands and configurations are presented (see attachment).

For the Docker Login (and Podman Login), if the value for the usernamen (-u) contains a $, this $ is escaped with \$, and the value ist enclosed in double quotes.

While this works for Linux (testet in Bash shell), this doesn't work for Windows.
Pasting the command in a Windows Terminal or PowerShell results in the following error message:

"Error response from daemon: Get "https://xxxx": unauthorized: Client login with unencrypted passwords is disabled. Please generate an encrypted password in the user admin panel for use here." 

While sadly the error message from the docker cli here is wrong, replacing

-u="\$app" 

with

-u='$app' 

makes the command work on Windows.
The modified command also still works on Linux (tested in Bash shell).