This project demonstrates configured icons using themes in Godot Engine 4.2.1.
The toolbar (toolbar.tscn) has a PlayButton (Button node) and a SearchBox (LineEdit node).
Both have a configured theme_type_variation property, which is set to Toolbar_PlayButton and Toolbar_SearchBox, respectively.
In the main.tscn scene, the top left and right toolbar child scenes are configured to use the theme_outline.tres and theme_solid.tres to customize the icons.
The Toolbar_PlayButton's base_type is set to Button, and its icon property is configured with a CompressedTexture2D of the res://icons/outline/play-circle.svg and res://icons/solid/play-circle.svg.
The Toolbar_SearchBox's base_type is set to LineEdit, and its right_icon property is also configured with a CompressedTexture2D of the res://icons/outline/magnifying-glass-circle.svg and res://icons/solid/magnifying-glass-circle.svg.
For comparison, the bottom two toolbar instances have editable children enabled and the PlayButton and SearchBox have their icon and right_icon (respectively) set directly to the CompressedTexture2D.
My expectation is that the top-row toolbar's SearchBox (LineEdit) would also show the magnifying class as configured in the theme.
Unfortunately, that is not the case.