Cutting a 2mm wide / 3mm deep groove

Is cutting bit 561 the smallest that is made that you can chuck into your Dremel? Find a narrower bit - it might not be made by Dremel.

Try a hobby store - model railroading/RC aircraft, not woodworking. They'll have absolutely tiny bits, there's bound to be something that will do the trick. It may take multiple passes to get to your desired width/depth. You might have to buy a whole new toy er, tool to do it, but if you really need a groove that small, that may well be what it takes.

You could also probably do it with a hand saw. I believe some of the Japanese saws are pretty thin, with some searching you could probably find one that fits the bill.

If you're absolutely sold on using the Dremel and can't find a cutter small enough, you may just be out of luck.

There is a whole world of CNC bits with 1/8" shanks that will work for this. Here's just one link: https://www.ebay.com/str/CARBIDE-PLUS/DIAMETER-070-0799/_i.html?_storecat=50046017013 You can probably find individual bits on Amazon or visit Kyocera online. As mentioned you should specify what material you're working with for more relevant replies.