The "auto" scrolling mode of the TabStrip works fine when we resize the container or the window - i.e. the scroll buttons appear if the tabs do not fit ij the container. However, they do not appear if we add tabs dynamically and this is a bug. If we add tabs dynamically, then once the tabs dont fit in the container, the scroll biuttons should appear. Below is the example in stackblitz:
https://stackblitz.com/edit/angular-p5jc7v?file=src%2Fapp%2Ftab_content.ts,src%2Fapp%2Fapp.component.ts
As you can see from the image below the tab strip tabs can keep getting added and they do not care where the parent DIV or any other container ends. It would be appropriate for them to allow for scrolling if it goes outside the width of its container.
This is the way it is handled in jQuery
https://demos.telerik.com/kendo-ui/tabstrip/scrollable-tabs