Once upon a time I used to use an old membrane keyboard with what I think were approximately Cherry profile keys, however unlike most Cherry keycaps I have seen, these had really soft rounded edges - no sharp transition.
I still have a set of heavily yellowed and worn keycaps like that. They are from a DytCom (Dah Yang) keyboard in Swedish ISO layout with Cherry MX Black switches. The keycaps were pad-printed ABS.
BTW. Have you tried DCS? It is somewhat similar to Cherry profile, except for rounded corners, more slanted bottom row(s) and a coarser texture on top.
The keycaps on the
BTC 15xx series rubber-dome (conductive dome, not membrane) keyboards have the same profile as DCS. The BTC were OEM:ed to lots of brands and very common so I think it is likely that the keyboard you remember was one of those.
The non-stabilised keys on the BTC are Cherry MX-compatible.
BTW. Welcome back after not posting for over ten years!