I can confirm both Skidpan's and BBD's observations by virtue of my own (old) 2005 build Mazda3 originally having 205/55 R16s fitted and changing the tyres and alloy wheels 4 years ago (due to replace the tyres anyway + corrosion/leakage issues with the then 12yo alloys) to 15in with 195/65 R15 tyres fitted.
I already knew that the ride was a good deal softer (but seemingly without noticeable penalty on handling) because a former workplace pool car was the same model but a lower-spec TS to my TS2 fitted with the same 15in tyres mine now has.
I don't regret doing this, especially as both (and especially) alloys and tyres are a reasonable amount cheaper, helped by both the old and new tyre sizes being amongst the most common around.
The 60 profile tyres BBD mentioned now fitted to the gen3 and 4 Mazda3s are a good compromise between my 16in OEMs and the higher profile 15in ones, having test driven a gen-3 car fitted with them in 2017. The ride on them was fine.
The current generation Mazda2 on the SE-L (Nav / +) spec (same for the base spec SE) comes shod as standard on 185/65 R15 tyres, which should give a decent ride. I drove one (an SE) as a courtesy car for a day a few years ago and I don't recall the ride being firm. Admitedly Mazdas tend to be on the firmer side as reagrds suspension.
The OP may need a VERY soft ride, so best for them to test drive the cars they narrow their list down to in order to see if they fit. Worth taking those test drives on a variety of roads, especially poorly surfaced ones, over speed humps, etc to really given the suspension and tyres a good test.
They may also find that like with mine, a car that otherwise meets their requirements could have the wheels and tyres changed (downsized) if the brakes can take them and the manufacturer allows it. They would need to inform their insurer, though it won't put up the premium, hopefully the opposite.
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