@Rayzon You have to have the Show Bookmark Bar option checked in Settings -> Bookmarks. Should also have it on Bookmark Icon Only.
Be aware that line 23, where it goes to hide the "weird chevron", div:nth-child(#) the # may change depending on how you've modified the main toolbar. Out of the box Vivaldi you want to hide # 6. You can find the number just by customizing your toolbar, and counting how many things along the icon is. Spaces count.
So if you, like me, remove the panels button and the flexi-space, you want to change it to a 4.