How does the whole inbreeding thing work? E.g. how is the percentage calculated, at what point are you unable to breed two pets, does it have any negative effects on stats etc.

First and most importantly, inbreeding has no negative effect on pets whatsoever.

You cannot breed pets with their parents, siblings, half-siblings, or children; however, they /can/ be bred with their grandparents, cousins, or grandchildren. Inbreeding increases when they're bred with those relations (or any more distant relations, too).

It's commonly found in trait breeding projects. For example:

https://www.sylestia.com/view/lineage/?pet_id=3272477

This pet is the result of one of my projects. I started with only three regular essences, two carries each, and bred up to four visible traits. As a result, every child of this project is inbred.

I can't tell you exactly how the percentage is calculated, just that it goes up when two related pets are bred with each other. But it doesn't hurt the pets in any way.

Thank you :)

it's calculated with the previous generations (up to 25 generations before) and with the amount of time ceartain pets are coming in the tree. Inbreeding dosn't have negative effect, it's just information.