Lackluster handling is sadly a characteristic of this platform and the 3/Ys in general. Mostly a function of the steering rack/column, then the OE suspension setup and finally the curb weight and how it behaves at or near the edge.
Sure you can go and replace almost everything in the suspension with MPP, UP, Redwood, Eibach, CamberKing, soon also SuperPro parts... but in most cases that will only create a track/auto-x toy and without careful consideration, unbalance or skew the car further in some direction. Its a tricky balance, specific to each driver and use.
Re thicker anti-sway bars with their floating hard bushings on this platform - opinions are subjective and mine is irrelevant - suffice it to say that either set greatly increases harshness over ill maintained road surfaces. Combined with the weight of the car, this alone mutes any improvement while cornering or quickly changing driving direction.
It also further amplifies the lackluster steering feel.
Not a fun experience for someone older and no longer interested in any type of spirited or performance oriented driving.
You can throw on some coilovers, control arms, trailing arms, etc but you will simply limit the practical use of the car to a few specific scenarios. Its too bad the aftermarket industry rarely ever embraces OE+.