Quick answer
Use egg prices and route timing, not made-up pet ranks
Current public coverage is good enough to tell players when egg progression changes, but it is not good enough to publish exact best-pet lists or hidden stat tables.
Public coverage currently names Basic Egg, Better Egg, and Dominus Egg. That is enough to explain when a pet purchase becomes part of progression.
The same source family also repeats rare Dominus pet and strongest player wording, but those remain demand signals, not ranking proof.