Fair responses.
To preface my perspective going into the GDD I visualized it as more of an Animal Crossing/Nintendogs/Neopets than a World of Warcraft so to speak. The game more heavily themes around the acquisition, breeding and training of pets rather than other larger MMO aspects like major story, combat, or grinding (As far as I saw. I'm aware mitigating grinding was a point in your document but that seems ironic with the systems in place to optimize your pets).
Soren Johnson once said, “Given the opportunity, players will optimize the fun out of a game”. Through breeding or holding on to high-value pets like the Fabled rating ones they may just win outright unless there are other considerable factors that prevent those things. Granted, your pets have personalities or dispositions that prevent them from learning certain skills more quickly, but what happens when any pet reaches the "ceiling" of its skill potential? Are the maximum numbers of points/stats for each creature the same? Do they vary by rarity or type?
On the subject of the in-game economics and greater scope of the game, addressing the economics first, your implementation of fee systems for different parts of the game could work, but some players may start running a "ranch" to sell optimized pets. And if fees scale too high cumulatively for a casual player to afford they may be permanently stuck at a point in the game because of always backtracking due to fees, will be dissuaded to play because it requires so much in game time and (ironically) grinding to keep up paying them, or the optimizers of your player base will see them as little more than minor inconveniences. It's not easy balancing Economics which is why some games have them scaled out of control (EVE Online and Team Fortress 2 for instance).
As for the MMO topic, your chats and gameplay loops consider this title a MMO but little information is presented about a greater story in the game. It doesn't need one perse if it's not meant to be a full MMO and more of a pet-based Stardew Valley but the implication of what an MMO is may shape your player's perceptions and find them disappointed that it wasn't the experience advertised. It could be re-branded to a Social Adventure game and take gameplay from inspirations like Pokemon Scarlet and Pokemon Violet. The story isn't mandatory but by interacting with the world and leading your entourage of pets you can create your own adventure somehow.
Those are all the thoughts I have at the time. I hope this helps you in your future development of the GDD and the project going forward!