I have got the following icons in the Figma file and I want to extract them as a whole as SVG, but when I click or control-click the border as well as the play icon, and choose copy as SVG, I only get the border (as shown below). How can I make copy the whole icon as an SVG or if it is even possible?
Make sure all objects are inside the group you selected. Alternatively you can to export the icon as SVG.
Select the whole group, make sure all objects are inside the selected group.
On the right side panel, in the Export section add an export format + and change it to SVG. Click on Export Group 1 (or whatever the name of your group) and you'll have the SVG with all elements.
Alternatively, instead of a group add all objects in a Frame (shortcut F) and export the frame. That way you can have some padding in your exported icon (useful to export square icons when the outer bounds are not in a square shape).