What bylaws does your building have in place regarding transfer of noise to other apartments and requiring sufficient noise insulation of flooring (excluding kitchens, laundries, bathrooms)? Not sure where you are, but in NSW it would be very strange for a strata not to have such bylaws, and I do not expect tiling could meet the requirements.
Plus, whether or not there was an approval of sorts in the long term past for another lot, I would agree with your strata manager that you would likely require a special bylaw to be drafted and registered – which will have to be voted on at a general meeting. And I feel you will struggle to get support from other owners to tile your entire apartment at a general meeting (i.e. if in my building you would need a very convincing case [in terms of both noise and maintenance/upkeep] for me to consider voting permission for this).
So in my opinion the right way to go would be to firstly consult your existing bylaws regarding noise and flooring changes. Potentially discuss with an acoustic engineer if the believe it will be possible to have sufficient noise insulation with tiling your apartment – if so arrange a report so you have something to show. And after all of that, if you want to proceed, talk to a strata lawyer about drafting a special bylaw as your strata manager suggested to table at the next EGM or AGM.
(On the balcony tiles question – it would generally be appropriate to let your OC know (via EC and/or strata manager) when you would expect to be doing this work due to the noise. Consult your bylaws as to whether there’s any additional requirements.)