Dremel4000 loud and excessive vibrations above 2500rpm

These symptoms are highly indicative of bearing issues. With these smaller size bearings, it's extremely difficult and unreliable to use 'feel by hand' method for checking bearing wear, as the bearing would have to be far beyond 'problem wear' level before it is bad enough to be hand-detectable roughness or slop. You will get excessive noise and vibration when the bearing is worn even at far less level than the wear required to detect by feel.

Greasing is also vital and key, however with you saying the motor had been very 'clogged' with debris, that almost guarantees that micro debris or abrasive particles did get into the bearings, so greasing them now would only be mixing new grease with the contaminants inside the bearings. However greasing them would (should) show you a change in noise/vibration, so at least you know the bearings are the source of the problem.
You 'might' somewhat remedy the noise/vibration issue by a thorough bearing cleaning and re-greasing, but it's likely you'll need new bearings.

The other issue with bearings is with looseness in both the solid front mount and the rubber-bushed rear mount.
A few laps of tape, trimmed nicely, around the bearing and between the rubber bushing (inside and out) often is used as a fix for any slop in the bearing-mount interface. Judge tape or number of wraps depending on your excess clearance, if any.

To 'Sell Private'... that part is the stator and I wouldn't recommend changing that as you'd just be throwing your money away, as that's the problem is far more likely to be an overlooked bearing issue, and extremely unlikely that the stator would be any part of your problem.

Man... I have similar on my 4000... There are at any speed random slight speed changes, which cause vibrations, I brought it to Dremel SC and they said I have to replace electric schema and the rotor shaft... half price of new tool.... ok I wanted mine to be fixed instead to I agreed, but the replacement parts did not fix problem :( I and SC had no idea what to do. Now I bought also new brushes, and casing... to exclude possibility something not tight ... again no changes - vibrations there and speed has 5% jumping time t time, I`m so angry I also want to try now replace last part - this big coil around the shaft.....

I've had the same problem, I bought a replacement motor from a Bosch Distributor and the New motor has a Higher pitch noise and Vibrate from 25-50% RPM 0-25% is very slow and manageable, Above 50% seems to find it's ballance. It's not much better than the defective one that needed replacing.