You should have had full boost at about 2200 rpm under full load. There is certainly no requirement to run the engine up to 4000 rpm to verify boost. In fact, the boost might fall off at 4000 rpm if you lift your foot to prevent overspeed of the engine.

My suspicion is that the wastgate is the culprit.

If the wastegate is partially open, even a bit, the turbo cannot provide full boost.

Now with regard to what caused a "worn out turbo" to limit boost, this is more complex. If the turbo is spinning freely, and if it reaches its design speeds, it is highly unlikely that it will not produce the desired boost pressure. This is true, even if the turbo is "worn out". Normally, they do not wear out. Their compressor and turbine wheels are perfectly suited to go 1 million miles and the bearings are the only thing that require replacement. However, there are exceptions. If any part of the wheels are damaged or missing then the unit will not function as designed. However, in this condition, the bearings will be taken out very quickly due to unbalance forces and you can easily feel this if you spin the impeller by hand (DO IT COLD!).

As mentioned above, I would carefully investigate whether the wastegate is fully closed, and the wastegate spring is working correctly, prior to doing anything to the turbo.