You can list the convo tabs at the left of the chat window so filling the area at the left is not easy at all. You have to open at least about 20 different chats, just to fill the smallest visible area only (which may freeze your computer
) If tabs are more than 20, only then you will have to use small arrows to slide tabs.
If you insist on using the tabs at the top of the window, then I can recommend you to display tabs with the smallest sizes.
You can find these options in "Tabbed Chats" preferences.
Also you can use the chat windows' taskbar menu to directly switch the convo that you want to.
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