Apple's Preview documentation distinguishes between Sketch and Draw.
Sketch can recognize a stroke as a geometric shape, which is consistent with your description of the pen tool interpreting your writing as shapes.
When Preview recognizes a shape, Apple says you can choose the original drawing from the palette that appears.
Apple also states that the Draw tool “appears only on computers with a Force Touch trackpad.”
Since your Mac mini does not have a built-in Force Touch trackpad, Apple's documentation does not indicate that the Draw tool should be available on your Mac mini.
That does not, however, establish that your Veikk A15 Pro cannot provide an equivalent freehand input method. Apple simply does not document the Draw tool as being available based on a third-party pen tablet.
You have already confirmed that the test PDF has full editing permissions, Force Quit Preview, and restarted your Mac.
The remaining question is whether Sketch is the only drawing tool available in your Preview configuration and whether there is another way to use the Veikk for genuine freehand writing.
If your goal is to write naturally with the Veikk pen rather than have Preview convert your strokes into shapes, the next step should be to determine what Preview and macOS 27 provide for that tablet specifically, rather than assuming the missing Draw tool is the cause.
Apple's documentation: Annotate a PDF in Preview on Mac