I wouldn’t panic at 3mm, but I’d start making plans. There are a lot of factors here. How many miles on the current pads, what was the original thickness. That can give you an idea of how many miles are left.
I’ll use my car as an example. The dealer told me that my rear pads were at 3mm, he lied but thats not the point. I don’t know why the mechanic would pull my rear wheels when the car was in for a takata air bag recall. But anyways, the car had about 100k on it. The OEM thickness is 16mm.
If the pads had really been at 3mm, that would mean I had worn 13mm off in 100k miles. That would be about 7700 miles per mm of wear. You can go to 1mm but you risk damaging your rotors. Any way, I figured I needed to replace them sometime in the next 10k miles.
It was spring and the weather was nice so I decided to go ahead and replace them. I ordered new pads from RockAuto and one fine day when it was particularly nice and I had nothing else to do, I replaced them. The most worn down rear pad still had 6mm left.
BTW, he also told me that I needed a new cabin filter. BS, I had just put a new one in. Everyone else in the waiting room was also told their rear brakes were at 3mm and they needed a new cabin filter.
Edit: I was doing an inspection on my daughters car and I noticed one of her rear pads was down to 3mm. For her I ordered pads and did them the next weekend. She is notoriously hard on brakes and I calculated that she had about six more weeks of life in them before they got too close for comfort.
Every case is different but I hope you have enough information to make good decision for yourself.