The button push would need to be a custom action that first writes the filter value to a user specific or user profile column before navigating to the tab. Then, you’d filter the list by that keyword.
Here’s a video of the filtering logic I use (does not include the button logic):
Glide: Filter an Inline List with Choice Components
It’s just that instead of using a choice component, you’d be writing the value using a set column action before the navigate to tab action.