How come everyone elses 350 has 4 pot calipers, but mine only has two pots???
Hoping for a picture of yours, showing the anti-rattle spring.
The spring should be pushing down on the top of the pads, pressing the pads down into the caliper
The pads are pressed down with the spring so they are compressed onto the pins. This should stop any up/down, or side to side movement, except against the spring pressure. In the picture above, note that the spring is in contact with the pads at the top in the middle (the "wedge" on the spring pushing down on them, against the pins).
This alone would stop any rattling if assembled correctly! (It is possible to install the springs upside down and therefore allow them to rattle
Also there should be a very small gap between the pads and the disk, 0.1mm to 0.5mm max (governed by the "flex" or"give" in the main seals). If ther is any more than that, then the pistons are not holding their forward position after braking, or are being forced back by runnout on the disks.