Not all things in Photoshop record in actions. Quick Export seems to be an extension or plug-in script part of generator and may not have action support programmed in.

Photoshop does not support SVG files well. If you open and SVG File in Photoshop it will open as a single raster layer no vector graphics are all. Thers is a third Party Plug-in the can open most if SVG layers as vector later in Photoshop. However, the plug-in does not support all that can be in an SVG file.
In Photoshop Save AS i do not see a SVG File type option.
There is an Export AS and it has a SVG option and it seems to be able to export a shape layers with path in the svg file and text as text style in the svg file which may open as a vector file in Illustrator. I do not install Illustrator.
I would suggest trying to record Export AS (SVG) in your action to see it the records for Quick Export you write does not record anything into an action. However ir did not one my Windows system. There is also a note in the Dialog that text may not render as expected.... Photoshop SVG support is not the best.