Once you set a flex-grow or/and flex-shrink within the content of a nestable tab it stops working and will just add the second tab’s content underneath.
EDIT; Once you make any changes to a block’s main settings the tabs completely stop functioning.
For example:
The tab content is shown and hidden with display: block and display: none. If you set it to display flex, it will always be shown (see screenshot).
Instead of applying the flex setting directly to the tab content, you can wrap your content elements again with a block or div, and make the settings there. This way the functionality of the tabs is preserved.