Yes, Talkatoo can be configured to show up on all of your desktops.
Multiple desktops are a feature of both Windows and macOS that allow you to have separate desktops, and configure certain applications to open on specific desktops. Segregating work and personal applications/browser windows is a common use.
Talkatoo will be visible on all of your Windows desktops with no additional configuration. It is not possible to have it show up on only one desktop, or in different locations on different desktops.
Depending on your settings and the version of macOS, Talkatoo may show up by default on all of your desktops, or it may be only on the first one.
If you need to adjust it, long press on the Talkatoo Icon on the toolbar, and choose the option under Assign to: All Desktops, or This Desktop.
Note that if you do not see Assign To and the options below, you need to ensure you have more desktops than screens. So if you have a laptop and second monitor, and 2 desktops, you would need to add one more desktop before seeing these options. See this site for more information: https://www.macworld.com/article/2990037/solve-mission-control-failing-to-allow-displays-as-spaces.html