Can you explain how it is that both a water supply and sewerage line are in the air space of your garage, and how the sewerage line services only your Lot?
In a way preempting your response, if you mean that both pipes are attached to the inside face of a wall, and that’s common / perimeter wall, and your sewerage line is integral with one that services the other two (2) Lots, then I’d agree with your Strata Manager.
However if the wall with the pipes attached is an internal / dividing wall within your Lot, and the sewerage line serving your Lot has a gully-trap at the point where it meets the one that services the other two (2) Lots, then I’d agree with NSW Land & Property Information.
Consider also that under either scenario, if the toilet pan is fixed to the floor of your garage, then technically it’s being attached to the common property and your Owners Corporation could require you to seek its consent to do that, although that would be a bit finickity in my opinion.
Either way, you’d need to use the services of a Licensed Plumber & Drainer and provide their License and Liability Insurance details to your Owners Corporation.