Use a single Use Browser/Application scope in Modern Design and perform all navigation steps inside it to stay in the same tab.
Use Navigate Browser activity instead of Open Browser to go to sub-pages.
After completing actions, use Navigate Browser again to return to the home page.
Keep a single Use Browser/Application activity in Init and store the output UI element in a variable.
Pass this variable into the Use Browser/Application in Process by selecting Input element so it attaches to the same tab.
This ensures all navigation happens in one tab without opening new windows.
The warning appears because when you pass an input element, Open property is ignored.
To fix it, disable Open and only use the Input Element argument to attach to the existing tab.
All navigation should then be handled with Navigate Browser inside that scope.