How would a new "clean sheet" General Aviation piston engine with all the latest technology differ from existing Continental/Lycoming types?
It would have a gearbox between the crankshaft and the propeller. That is certain.

Other very likely details would be:


overhead camshafts
four valves per cylinder
water cooling at least for the cylinder heads
electronic ignition
single lever control


This would enable it to run constantly at about 4000 RPM and create the same power from a smaller displacement. The consequence would be a more compact and lighter core engine. Compared to a car engine, the cooling system would be more capable, so the weight would still be higher than that of a car engine of the same nominal shaft horsepower. But it should be lighter and allow for a more aerodynamic cowling than the current piston aero engines.

The Porsche flight motor (PFM 3200) was like that, and for a reason. Yes, it did not outperform the older engines in terms of mass, but it was noticeably less noisy. Starting from a dated six-cylinder boxer design, the engineers could not fully optimize the engine for its intended purpose.

Once a gearbox is fitted, it makes sense to reduce propeller speed, so the diameter  of the propeller fitted to that engine would be a bit larger than that of a comparable propeller on a conventional engine.

Once Jet-A is widely available at GA airfields, a diesel version would also be very likely. Note, however, that the system weight of a piston engine (engine + accessories + fuel system + fuel) will be higher for a diesel on short ranges.