I really do like what's here so far. It definitely feels pretty complete. A few notes though.
I found it most optimal to play without unlocking other ingredients, particularly in Milky Mode. I would also like to suggest that each ingredient's tool tip is displayed whenever it's hovered, unlocked or not, so players can better expect what unlocking the ingredient will do.
Milky Mode's effects are certainly appreciable. However, after a certain point, the production is practically an instant max out at any size. I'd like to suggest a hard cap on how high milk production can go. This is more for Milky Mode rather than standard gameplay. Additionally, I want to suggest that when playing in Milky Mode, you can't buy the "increase production" upgrade
Similarly, there's really no point to the "reduce production" upgrade. Each tick of Milky Mode is of equal effect, and easily outpaces your gains to buying the upgrade. And during regular gameplay, you have no need for it. It should be removed/replaced. My only thought is "Orgasmic Touch" upgrade which further increases happiness when the barista is milked.
I think a "sandbox" mode would also be nice. But I understand if you don't want to add that.
I would like to see more customization options for the Barista, like hair color, hair style and skin tone. Those particular upgrades would be free regardless of mode.
Last but not least, I think milking your barista enough should result in an order of 100% breast milk, at least in Milky Mode as a result of the current state. I still think the production should be capped, but (I think) that cap should still be high enough to allow an almost instant maxing out.