MSDF has no effect on tooltips

[ghost]

Godot version

4.0.3

System information

Windows 10

Issue description

Using a font with multichannel signed distance field enabled has no effect on tooltips:

Steps to reproduce

1 - Add a Label node;
2 - Add text to the "tooltip_text" field;
3 - Set "mouse_filter" to Control.MOUSE_FILTER_STOP;
4 - Add a theme to the Label;
5 - Add the "TooltipLabel" type to the theme;
6 - Set a font with MSDF enabled in the "font" property;
7 - Run the project;
8 - Hover the Label with the mouse.

Minimal reproduction project

tooltip_msdf.zip

[Calinou]

• Duplicate of Popups (OptionButton, tooltips) placed and scaled wrong when using canvas_items stretch mode or scale factor different from 1.0 (DisplayServer regression) #54030.

MSDF works on tooltips (notice the lack of font hinting in the tooltip), but tooltips are rendered at a lower resolution than the rest of the window. Notice how the popup's corners (which are drawn with a polygon-based StyleBoxFlat) are blurry as well.