The March has finished; lest we forget!
Your Plan is post 1974, so we can ignore one complication at least.
Regrettably, like any legislation, the NSW Strata Schemes Management Act contains few specifics and rather provides the principles upon which Strata Schemes are managed, and in your case those principles dictate that Owners Corporations (O/C) are responsible for the maintenance and repair of Common Property and Owners are responsible for that with regard to the area within their Lots.
So in your situation, an accepted interpretation of those principles (not just mine) would make the rectification of the leakage in the small pipe under the sink your responsibility as it’s within the cubic air-space of your Lot, and any confirmed leakage from the bath lip similarly your responsibility as, albeit original, the lip and any waterproofing behind it is against an internal wall of your Lot as opposed to a common wall.
However (there’s always at least one of those in Strata) in situations such as yours where water leakage from your Lot is affecting the Common Property and/or another Lot and it’s not from an obvious source within your Lot (such as a dishwasher hose) then it is customary, and indeed in the O/C’s best interests in terms of it preserving the integrity of its Common Property, for it to do whatever is necessary to determine the source of the leakage and to make necessary repairs, and then only if it’s confirmed as being from Lot property to at its discretion pass its costs of making the repairs to the Lot Owner. It’s much less common, and as you’ve found out messier, for O/Cs to do as yours has done by determining the source (reportedly) of the leakage and then encouraging the Lot Owner to directly arrange and pay for those repairs, especially with a different tradseperson.
Again in your situation, any damage that’s caused to your Lot (such as to wall tiles) as a consequence of the O/C determining the source of the leakage must be rectified by it; not by you as the Lot Owner.
It seems that your O/C was heading down the correct path until, albeit on the advice of its plumber, it determined that the source of the leakage was from within your Lot and you, with the benefit of hindsight, made the mistake to at that early stage engage your own tradespeople to repair the reported leak around the bath lip, which I’m guessing occurs because your shower is above the bath (?).
All of this merely confirms why you’re now in the situation you’re in; so what to do now?
I’d suggest you don’t contact the strata plumbers or their insurers (you didn’t engage them), but instead advise your O/C in writing that you’ve to date acted in good faith by accepting its advice concerning the source of the leakage, by accepting its offer to permit you to directly engage the services of tradespeople to rectify a problem that it had advised you was the source of the leakage, but that due to your concerns about the possible impacts of the on-going water leakage upon your Lot, the Lot below, and the Common Property from now on you’ll be relying upon the O/C to conduct whatever further investigations it deems necessary to properly identify the source of the leakage, and to permanently rectify that and all existing and any future damage that’s consequentially caused to your Lot.
I’d further advise your O/C that should it now determine that the source of the leakage is from anywhere other than the bath lip as it previously advised or if its investigative works adversely affect the works / warranty that you’ve paid for, then any further costs that it may resolve to pass-on to you will be adjusted before any payment to account for the amounts that you’ve already expended on the basis of that advice.
Probably not entirely the answer that you wanted, but at least you won’t be throwing any more money at a problem that your O/C should in the circumstances be chasing-down.