Why is my 50-600V voltage tester able to detect 3V?
plugging it into a 120V outlet means there should be a 3V drop across each bulb, so my 50-600V tester shouldn't be able to detect that

Your tester is not detecting the voltage drop across a bulb, but rather that of the AC electric field produced by the &quot;hot&quot; lead of the system.
If the geometry of the system were other than it is, such that there could be a place where the tester were near only the &quot;cold&quot; end of the string just a few bulbs up from the neutral, then it's possible that at that point there might be insufficient field strength to activate the detector.  But the usual design of these folds the loop, so there is no such place.
Additionally, just because the tester is hoped to detect 50 volts or more does not mean it will not detect less, doing so is simply not within the stated design goals.