All pets page - a mix of what we see on "Explore" but all on one page (I have more than 6 pets) and the individual pet pop-out window, along with their "location" if away (ex. exploring a planet, searching for treasure, etc). I'd make a mock up but I'm recovering from hand surgery right now and am taking it easy while healing ^^;

Better TU payout for Bird Quest - Those cages are expensive, and the occasional Relking Coin aside I have no idea what the prize items (leaf scrolls) are even for that might make them worth doing.

A quest for "natural" pets / another quest for training tokens - this could be 1 suggestion or 2.

Alert notification when pet finishes resting after exploring - a couple hours is just long enough for me to forget about it lol

NPC shop item sorting by amount of effect - ex. amount of food an item fills when eaten, or intelligence points a book gives when read. obviously not for all shops, just those with consumable effect items.

Overhaul Library/Squishy Shelves - allow searching, sorting (by +stat amount, if used by current active pet), increased number of items per page, and a Book Log of which pet last read a book before it got worn out/broken (do squishies do this too? I don't use that one lol). Having your library and squishy collections visible/linked on profiles would be nice too. 

Planet Residence Visa(?) - this could be a cash shop item that temporarily lets you live on said planet for a certain time (week or month?). Ideal maybe for folks like me that want to just check out the exclusive planet quests and daily activities to see if it's worth switching but want a bit longer time than the RC candles.

Obligatory pet species suggestions: Seal/Sea Lion/Walrus (ideally not hybridized with something else), Imp/Demon/Devil/Gargoyle, a Viper or Python-type snake, Mothman/cryptid-insectoid, Eastern Dragon