Just an FYI, I was curious about the audio lag on phone calls. I thought I had noticed this during one call (but not so much during a second call). I think the only way you would really detect this is if you notice awkward pauses and talking over each other during a conversation (which certainly isn't unique to technical problems). Anyway, I used a "call echo" phone service and manually timed it with a stop watch. I ran 3 different configurations and timed it several times each, and here's what I found. This is an iPhone 13 Pro with a 2021 Telly SXP:
Phone without
Carplay at all, using iPhone's speakerphone: about 700ms between when I spoke and when I heard the echo (roundtrip time)
Phone with wired
Carplay, using car's microphone/speaker: about 800ms
Phone with wireless Carlinkit, using car's microphone/speaker: 1400ms
So there is some added latency and Carlinkit adds about 600-700ms to the roundtrip time. Assuming this added time is split evenly between outgoing and incoming sounds, It means that it takes about 300-350ms longer for people to hear what you say on the phone compared to a non-Carlinkit setup (and also adds the same to you hearing what they say).
Admittedly these numbers are not super precise, as it's hand-timed using maybe 10 tests per configuration. They're not averaged, just the result of where I think it landed after doing this over and over in each config. If I averaged them then I think it would be biased toward longer response times because I can only stop the counter so fast after I hear the echo response.
The numbers themselves don't mean much to me other than top confirm that the Carlinkit does add a meaningful amount of latency to phone calls. Ultimately you'll know it when you experience it, and I'm still undecided if it actually bothers me or impacts conversations.