Car Bluetooth reacts to iPhone input with ~3 s delay—why?

There is no setting which will do anything on your iPhone. And your assertion it has nothing to do with the cars infotainment system isn't quite accurate. Bluetooth and wired aren't the same connection. You have a 10 year old car, with Bluetooth that is now several generations behind in Bluetooth versions. Whether Acura can update the infotainment system in your car is questionable. Infotainment systems from a decade ago, often weren't software updatable.

You can check with Acura and see, but this wouldn't be an iPhone issue.

D. Hoffmann wrote:

I disagree that it could not be an iPhone issue. If I tap on the Pause control in the Podcasts app, the iPhone would immediately stop sending the audio stream via Bluetooth. At that point, because the infotainment system is not receiving anything, anymore, it should also quit playing audio.

The behavior is closer to the iPhone buffering 2.5–3 s of audio to be sent via Bluetooth.

OK, but I still maintain you're dealing with a car's infotainment system which was designed more than a decade ago. A LOT has changed in more than a decade. While there is no way to validate this is an iPhone issue I'd be willing to bet if you connected your phone to a much newer, more modern car via Bluetooth, this wouldn't be an issue. The bottom line is there is no setting you can change on your iPhone.

if it's an iphone issue then it would likely be present on all vehicles around

if it's an issue for other iphones and maybe android phones, then it could be slow bluetooth processing power on that type of vehicles bluetooth system.

D. Hoffmann wrote:

I used Bluetooth input, because I wanted to be able to connect wirelessly. I have a windshield-mounted MagSafe iPhone holder. I like the convenience of being able to just plop it on there and have it charge and connect to the infotainment system.

Cable also gives you a charge while using it. BT is not really of use apart from phone calls, and if you upgrade the car to a 2020s Carplay setup, cable will still be the optimal quality option.

It has been a while so I'm not sure what happens to phone calls when ipod/cable connected

Selecting iPod is the correct way, how were you doing it before?