This is a great question, and had to think about it, but I think I have a simple solution:

 1. Go to *Draw Mode*
 2. With the box tool draw a rectangle at any location and orientation you want in the 3D Viewport.
 3. Hit <kbd>Enter</kbd> to confirm the box location, orientation, size
 4. Optional: change your view so you can understand this technique is not dependent on world view
 5. Enter *Edit Mode*
 6. With the *Selection Tool* active set the *Selection Mode* to *Select Only Points* or *Select all Stroke Point*

[![enter image description here][1]][1]

 7. Select the whole rectangle you just created
 
 1. Now switch the *Cursor* tool
 2. With the *Cursor* tool selected go to the tools *Settings* and and set the *Transformation Orientaion* to *Local*

[![enter image description here][2]][2]

 3. From the 3D Viewport Menu chose *Grease Pencil > Snap > Cursor To Selected* (you can also use the shortcut key: <kbd>Shift</kbd> + <kbd>S</kbd>  )

[![enter image description here][3]][3]

 1. Go back to *Draw Mode*
 2. Draw with any tool on the rectangle and then move your view to see that the strokes are in the same drawing plane.

You can see the drawing plane by turning on the 3D Canvas in the *Viewport Overlay* (In the *Edit Grease Pencil* section, put a checkmark next to *Canvas* to turn it on)

  [1]: https://i.sstatic.net/3b3wM.png
  [2]: https://i.sstatic.net/tg9Xf.png
  [3]: https://i.sstatic.net/x5aXs.png