To be honest, if you're sure there's no difference at all between it being on and off then it's certainly possible it could be broken, the video I linked was pretty much exactly how I remember IS (on Canon anyway) and I don't think there's that much difference between them,
But tbh - 1/30th, handheld with a 3KG telephoto, I'd be impressed if one in ten shots were acceptably sharp, even with the best IS.
This, your effective focal length is 400mm (250mm x 1.6 canon crop). Hand the rough rule of thumb would be 1/400th. Personally I would aim for 1/500th second as baseline, especially with a 3kg piece of glass.
IS/OS will give about 2 stops most of the time, so that is about 1/125th of second. With good technique and a very well working stabilization system you might get to 1/60th.
1/30th is still another whole stop away and even with good technique and excellent OS that is too much. One thing about OS is that is can actually make things worse when you are not in the correct operating range. Shutter speeds too high or shutter speeds to low will likely increase blur.
I would take some shots at 1/125th second at 250mm with OS on and off and see where you are (or at 300mm and 1/250th second).
OS/IS/VR is not some kind or miracle, as I told you before if you want high acuity then you need to use a decent tripod.
Also if you are not used to long lenses then thee is lot of technique to learn and with such a big lens you need to build up strength. Quite a few of the wildlife pros do marathon training and do weights several times a week because they might have to trek 10-20miles into the wilderness ad hold 4Kg camera setups for extending periods.
And it is not just about strength, it is mostly technique. A lot to do with breathing, half holding shutter etc. When I first started using my 300mm f/4.0 with 1.4xTC (so 630mm FF equivalent) I rarely got good shots. With time, practice and getting high shutter speeds (1/600th second) I managed to get the results I wanted.