Tabs
Two treatments for two jobs. Underline tabs navigate between sections of a page. Segmented tabs switch how one dataset is displayed. Using the wrong one makes a view switch look like navigation, and people lose their place.
Underline
Arrow keys move between tabs and only the selected tab is in the tab order — that is the roving tabindex pattern, and it is what the ARIA tablist spec expects. Without it, a ten-tab bar costs ten Tab presses to walk past.
Selected: runs
Segmented
Sits inside a toolbar next to other controls, so it gets a contained shell rather than a full-width rule.
Counts
A count belongs on a tab only when it is stable enough to be worth reading. A number that changes every poll turns into visual noise and trains people to ignore the whole bar — which is the opposite of why you added it.