You could keep the stock springs and upgrade other areas.
Easiest to do would be performance shocks and upgraded rear shock mounts, especially the rear upper mounts. Monroe makes some harder rubber ones that are cheap. Upper are part # 907984 and lower are part # 907985. In the front, you could upgrade to M3 control arms.
https://www.ecstuning.com/b-trw-part...3322283547kt4/
You could also add camber kits in front (these replace the stock upper shock mounts) to dial in an alignment with more negative camber which will improve steering response and grip.
More labor involved would be to replace the rear subframe bushings, which are also part of the cause of rear end floatiness. You have to drop the subframe to do this. Whiteline makes a kit (part # KDT917) cheaper and easier to install than M3 subframe bushings while also being stiffer. I have it on my car. The rear end is much more consistent feeling than stock.
Replacing the rear sway bar also requires lowering the subframe so if you do the subframe bushings, it's a good time to also do the sway bars. If you want the car to be more tail-happy you would go for a larger relative increase of rear sway bar vs. front, so personally I would not just add a rear sway bar to a rwd E9x. From most to least tail-happy of the front & rear sway bar combos, you have H&R and Whiteline at 27mm F/20mm R, Eibach at 28mm/15mm, and Hotchkis at 32mm/16mm. With stock springs, I would probably go with H&R or Whiteline sway bars, or Eibach if you want a bit more conservative setup. The Hotchkis front bar is huge so their set is a better match for springs or coilovers which have relatively stiffer rear springs.
Point being, if you like your stock sport package ride height and spring rates, you could do
plenty of upgrades while keeping the stock springs.