CdA values in the 0.2-0.22 range are very low - you’re into the territory of pros or extremely keen amateurs who have spent time in the wind tunnel and a lot of effort to optimise every last detail of their position, equipment and kit. A more normal CdA for somebody who’s ticked off the low hanging fruit (had a professional fitting, aero helmet, race wheels, snug fitting suit, etc) but not gone further is more likely to be in the 0.25-0.3 range. So if your friend is towards the top of that and you’ve got a very aero road position then your results would be fairly similar. Could also be that you had other advantages e.g. better wheels, tires, handling, etc. Even a single turnaround point on an out and back course can be enough to make up quite a few seconds if you’ve got a good handler on a road bike vs a rider who doesn’t ride their TT bike on technical bends too much.
Other factor is length of event, a big advantage of the TT position is that by resting your elbows your upper body is supported skeletally instead of muscularly. I can hold a TT position comfortably a lot longer than I can hold an aggressive drops position. Doesn’t really factor into a 20 minute event, but the longer you go the more of an advantage the TT bike has. Particularly if it’s a triathlon and you have to run afterwards, in which case having tense/tired arms and shoulders from holding a drops position can really slow you down.
I think to gain a significant advantage over a short TT like this (compared to a good drops position on an aero road bike with good deep wheels - i.e. your setup) you need to not only have a TT bike but also spend a good amount of time riding it to nail the position and handling, and a good amount of effort optimising your setup. So if you do the occasional short TT it’s not worth the investment. And you could likely save quite a bit of time from your current setup for a lot less money than a new bike if you invested in an aero helmet, a skinsuit, aero shoe covers, maybe a rear disc (or borrow one).