When you publish your application as a PWA and it runs in the cloud, you should receive extra Navigation profiles. Based on these Navigation profiles, you could determine the page and therefor the buttons that are on the page.
More information can be found here: https://docs.mendix.com/refguide/progressive-web-app
Hope this helps!
You can use classes on a container or button to hide on desktop, tablet or phone devices. Check out the appearance tab of your button properties