Do iFixit Batteries Pass Apple's Validation?

Apple introduced parts serialization in most of their products similar to what John Deere did within its tractors and accessories

The iPhone 14 Continues Apple’s Digital Repair Lockdown which your phone also has.

There was a huge push pack on the practice and Apple has relented a bit! So instead of making a brick out of your phone, with the newer iOS releases one can bypass the pain using 3rd party or even real Apple parts recovered from a parts phone.

Here's a deeper writeup Parts serialisation on Apple iPhones this is a bit dated as Apple does now sell parts directly to people via their Self Service Repair program as well as the tools Apple uses or rent for the bigger tools if you want to be exact in the process. In truth there are cheaper options than using Apples tools and jigs which also will work on other devices.

Now getting to your exact question as I stated at the beginning even Apples own parts will be seen as alien to your phone until the phones serial number database is updated which your phone requires. Older series had different issues which I think is where you got a bit of confusion.

So here's the guide iPhone 13 Pro Battery Replacement and the needed part from iFixit iPhone 13 Pro Battery

Do take the time to review the guide and the needed iOS level to run Repair Assistant service built-in to the iOS services to properly introduce the replacement battery.