Is it possible? I mean for example, suppose that I have added a weirdly angled plane like image 1. I switched to “Global” coordinate to the “Local” coordinate of the plane like image 2. Now, I add a text and its rotation is 0,0,0, but it is not aligned to the plane. That is, that rotation is still in global. If I try to move the text, it seems to be moving in the coordinate of the plane, but can I make the values like rotation be displayed in the local coordinate of the plane, too, so that 0,0,0 would mean the same rotation as the plane?
I’m not sure exactly how those custom orientation works (hopefully someone comes by and explains). It will create a… uh… sort of a snapshot (?) orientation from current rotation.
I see here an operation in Object > Align to Transform Orientation - looks like it rotates the selected object to selected Orientation. For location you can Snap a selected object to Active (or Cursor).
The coordinates will still be in Global coordinate System however.
Depending on what you’re trying to achieve, maybe Parenting is a better option? A parented object will have its coordinates in a Local system of another object that you can see in Transforms.
Or Snapping (manually)?
see also 