Packaging development is a very important part of a medical device project, and in my company, we have engineers who are dedicated to package development. For packaging, and especially sterile packaging, the tests that are performed are usually very standardized, and the packaging engineer does not have to define new tests each time we are developing a new product. We often rely on our packaging suppliers to develop the testing protocols, which includes the test procedure, and these protocols are then reviewed and signed by representatives from my company. Some common packaging tests include real time and accelerated aging, ship testing, and sterile barrier testing. The procedures are defined based on an ASTM standard or some other standard, and I have listed several ASTM standards below if you would like more info.

ASTM F1980: Standard Guide for Accelerated Aging of Sterile Barrier Systems for Medical Devices
ASTM D4332: Standard Practice for Conditioning Containers, Packages, or Packaging Components for Testing
ASTM F2096: Detecting Gross Leaks in Medical Packaging by Internal Pressurization (Bubble Test)
ASTM F88/88m-09: Standard Test for Seal Strength of Flexible Barrier Materials (Peel Test)