How to suppress print in only in front page via twig
You can have as many differen view modes as you want, both the frontpage and the term pages by default are views, so they are easy to customize.

So create a new one under Admin > Structure > Display modes, then enable it for that node type and configure the fields as you want. Then change one of the views to use that view mode.

Another option would be logic in process, but then you need to add the right cache context.

Or you just hide that field with CSS.