Siri on CarPlay's gotten "hard of hearing": Misses first word or 2 of text dictation, can't always hear "yes" or "no" confirmations

Starting with iOS 16, Siri on CarPlay has had issues hearing the start of my dictation prompts, as well as the "yes" or "no" confirmations before sending messages.

I'm using an iPhone 14 Pro Max, currently on iOS 16.2, though I believe this issue began with iOS 16. I am using CarPlay on a 2019 Toyota C-HR, though I have experienced the same issue on my daughter's 2014 Corolla, which has a newer Kenwood audio system that supports CarPlay. Changing cables doesn't fix it, either.

I'll start a message by either tapping the screen or asking Siri to send someone a message. I dictate the message, and sometimes the first word or two is not picked up. For example, I might say, "I am going to the store after work," but Siri reports back "going to the store after work." It does this maybe a third to half the time I use it.

More frequently, after Siri speaks my message for confirmation, it doesn't hear the yes or no when I say it. I have to repeat it. This happens more than half the time. I notice that if I wait a couple of beats after the chime, it does hear me.

I'm a longtime CarPlay user and this behavior is new in this vehicle. It's possible it's my phone, but Siri on the phone doesn't have this behavior when using it outside of CarPlay.