Glad to hear this is getting addressed! I may be missing some others that should be included (I know videos are handled on a per-website embed basis but they count here too!) but expanding on these: Every independent element for designing content within the editor should be available in the quick add menu.
But hey, why stop there?
The “Quick Add” menu currently acts the way the tools panel does in Adobe Photoshop / Illustrator, the node shelf in Nuke, or the toolbar in Figma. If I were making this software (which I’m not so hey, this is one guy’s opinion) I would take this one step further by separating these from the other template elements and treating them the same established way that tools are traditionally treated in design software, by showing them to the user at all times. This means that users who aren’t exclusively using your pre-built elements save a click every time from closing a menu and opening up the “add elements” panel which currently also takes up a lot of visual real-estate.
Replacing this menu that takes up 27% of the screen space to display 15 tool icons would be the way to go in my opinion. It does a good job at displaying template elements but the vast majority of the time I don’t use or need those and it really slows me down.