Bug 453142

This isn't likely what you wanted but it can be done in the Konsole settings, you can see a .css file that should allow what you want.  I'm open to other suggestions on how to do this.

https://docs.kde.org/stable5/en/konsole/konsole/tabbarstylsheet.html

A workaround is better than nothing.

Can you reproduce or should I add a screenshot how it looks here?
I have on the tab bar with Plastique theme:
- 1-3 px lightgrey border above inactive tabs and the active tab is connected to the top border of the other tabs
- Inactive tabs have a gradient with two light greys, the active tab has one solid lightgrey
- The active tab is slightly higher overlapping the area below

While this is visible when looking at the tab bar directly, it is hard to intuitively notice when looking at the terminal contents.

I think we should not workaround style issues in the applications, Kate and Co. use the normal tabs, too.

At least for the KDE Plasma default style it looks ok for me in the current version, if other styles have issues, please report that there.

I think konsole was the only program where I ever noticed that problem. But thinking about it, I guess the point is that not too many KDE program (I use) have tabs. I can compare with Falkon which has the difference that the active tab is merged with the UI under it (both grey, while console has the terminal background color there and only like 1 or 2 px padding in between) and that it has close buttons that may also be a visual indicator where a tab ends. But I am not too fond of close buttons myself for when one gets many tabs. Otherwise it is hard to tell as falkon has tabs on top and konsole tabs on bottom.