Hey TheWoldsMan,
Updates recently released that could resolve this issue. If you haven't already, take a moment to back up your iPhone then update the software and apps:
How to back up your iPhone, iPad, and iPod touch - Apple Support
Update your iPhone or iPad - Apple Support
How to manually update apps on your Apple device - Apple Support
In addition to updating, make sure the photo library has finished indexing to show this change. Those details can be found in the guide you recently viewed here: If you can’t find pets in the People & Pets album in Photos - Apple Support
For your photos and videos of your pets to appear in this album, your device has to first complete the following steps:
1. Index your photo library.
2. Find pet images.
Your iPhone or iPad must be locked and connected to power during the detection process. Photos on your Mac can detect these photos as long as you aren't using the app. Depending on what tasks are running in the background and the size of your photo library, this process could happen quickly or take up to a few days to complete.
While the Photos app is detecting pet photos, a "Finding People..." message appears in the People & Pets album. Until this detection is complete and the pets in your photos have been identified, the album will still be labeled People instead of People & Pets.
Fix misidentifications, remove people or pets, and do more with the People & Pets album in Photos
Let us know how it goes.
Take care!