Welcome to the jungle, join the few, the shamed, those with inexplicable wireless Carplay connection issues related to remote starting. There are several threads in here (try the forum search). For me wireless carplay worked fine for 2-23 months. Then, with after App remote start, I would have to go to settings/bluetooth/select wireless Carplay. Then that stopped working. I would "Forget" (un-pair), then re-pair bluetooth. That was fine until my next remote start with App or fob. Rinse and repeat. It takes a lot of time to do that, and every time I used any form of remote start wireless would not work and I would go back to 2020 nd use my cord. Oh, and BTW, Toyota's Nav system stinks, it shows traffic jams as clear green roadways (at least in St. Louis) most of the time, though sometimes it will go all the way to yellow.
Oddly, it sometimes works. Lots of theories on here on how to make it work:
For me, I "think" that if I turn the radio off (push volume button) before shutting my engine off, remote start, after after pushing "start/pedal", wait a few secs, then turn the radio on, it will either connect, or I can go into settings, select BT, select Carplay, and it will connect. Sometimes, it just works. And sometimes, not. I think Toyota has a software bug that manifests in a subset of Apple phones, subset of Apple phone settings, or a subset of their BT firmware.
One forum member thinks those of us with wireless Carplay issues are the problem ourselves, we have our phones set up wrong. I don't agree, as I have a lot of experience setting up wireless devices and have never run into a connection headwind like this, and not with any of the 20-30 rental cars I have used over the last 12-18 months, all makes, models. But maybe they are right, who knows.
One day, one of us will find a solution. In the meantime, I suggest having a cord handy for when you really need Nav, phone, etc.