Here are some solutions fir you that you might not know about.
1: pushing T instantly transfers the item from one inventory to the other. So if you search Thatch and all your thatch filters, just hit T a few times.
2: if an inventory is full, adding more of an item will force it to stack with any existing items in the inventory. So say you have a large box of 19 Raw Meat in each, hit T over a meat in your inventory and it'll start forcing them over to complete the stacks.
3: dragging one stack over another stack in YOUR inventory will cause them to combine. This does not work in boxes.
4: holding shift splits a stack in half, holding cltr splits off 1. This also works with the T command.
I have found in select cases that it's beneficial for things not to auto stack, as as since in your personal inventory of a pet's it's affected by weight and not stack limit, this seems like a trivial point to me with the current already implimenting mechanics.