The biggest aero gain of my aero road bike (a 3T Strada) is that it puts me in a more aggressive position. That gain is very real, but has zero to do with tube shapes.
That’s an excellent point, because it tells you what you can gain on a “regular” frame (almost all carbon frames these days have some aero features) you need to upgrade wheels and cockpit and get most of the gains of a “full” aero bike.
The only other and arguably more important aero gain is taking something like a yoga course so that you can sustain a more aero body position for longer on the bike.