We can hardly read the numbers.

I suggest the following two changes:

• If the tab is not selected:
  we show the badge as outline with a number in it, similar to how we show the inactive help text icon in forms.
  we use a darker gray (try color <12>: #A3A3A3)

• If the tab is selected, we show the badge in black instead of leaving it in light gray. For this, we either use the same outline icon as above or we use the inverted one used in the screenshot below - we'll have to see how this looks.