Unfortunately level of detail comes down to bit size. With a 3mm end mill all x and y corners will get a 1.5mm radius.
When you get the hang of things a bit more, you can rough out most of the wood with a large mill, then do the final pass with a smaller one for more detail and faster milling times.
If you check out some big machines youll see they actually have a turrent of bits, up to 30 or so. All to achieve different things.they will typiccally use 5 or so different bits per part.
Take it slow, make a few cuts, try some different objects. You’ll learn quick. The one you chose to learn on is actually a 2.5D part and actually not very suited for milling. I need to find a cool part amd do a walkthrough. If you check the videos page you’ll see a new video where he made a rose relief and changed bits in the middle. The part came out great. Might give a better inderstanding of what I’m try to describe.
Feel free to ask questions.