Once you move in, you can always save up for a year or two, rip out the drywall, put in some insulation and remount the drywall on resilient channels. Windows generally aren't a problem since even the crappiest code-minimum windows are pretty good these days. Floors are a challenge though, unless you can convince downstairs neighbors to put in some insulation or just straight up pay for it yourself.

I suspect that they aren't objecting to the sound proofing itself, but an architectural change of using a different style of windows than the rest of the units.

That's my suspicion too--the most airtight and thus soundproof windows are casements, which are common in continental Europe but less so in Anglophone countries where sash windows dominate, and HOAs (as well as historical preservation committees--the bane of energy efficient retrofits everywhere) often take a dim view of replacing the latter with the former.

We live in a flat that is in ~1800 townhouse that was converted to flats about ~1900. Have never heard a single noise from neighbours (external walls are 1m sandstone!). We also have original shutters on most windows which do a lot to overcome the weaknesses of old sash windows.