The plate itself should be pinched very securely on the axle between the #4 axle spacer and the swingarm, so the plate shouldn't move at all. Note that the #10 pieces between the plate and caliber are rubber and there are no bolts or nuts securing the caliper to the plate. I believe that caliper movement relative to the plate is deliberate; that the caliper floats slightly so minor disc thickness variations and/or warping don't cause pulsating brakes. I just checked my rear plate and caliper; my plate doesn't move at all, but I do have slight movement of the caliper relative to the plate. Depending on where I measure it, I'm also getting 1-2mm of movement (at 39,459 miles). So, as long as your brakes are working normally, I think you're fine.

Note: The #10 pieces are offered as a "Repair Kit, Rubber Cover". At some point, that rubber gets old and worn enough to merit replacement.

 

The caliper is/must slide and move. This is a single piston setup. The piston pushes and that causes caliper slide so the pads move towards each other.

If this were a fixed caliper/dual piston setup then yes the caliper should not move.

 

It never crossed my mind that it was a single piston, too used to working on pedal bikes 🙄.
Thanks for the help 👌.

 

Put pressure on the brake pedal and see if the caliper goes solid.