This is the old "how do I take an action when I click on a button in Power Apps" question. Everyone struggles with this when they get started, and the solution is that we need to think more like excel, and less like other programming environments.
The button click won't filter the gallery, instead let's set the "new" button to set a variable that contains the value "new", the "in progress" button will set that same variable to have the value "in progress", etc. Then, we can set the gallery to use that variable as part of its filter.
So the new button will have:
UpdateContext({varStatus:"New"})
And the gallery can have the following as its items property:
Filter(tablename,Status=varStatus)
IF your status field is a choice field in sharepoint, we'll need to take that into account to reference the value of the choice field:
Filter(tablename,Status.Value=varStatus)
