It's orthangonal until however you're charging it can't keep up with demand. A 14 Max on a standard USB-A -> Lightning connection is already really marginal. Like, I can drive for an hour with waze running and the phone plugging in (wired carplay) and it'll charge maybe 5%.
What kind of amperage is your car putting out? Older cars really struggle to power phones. In some cars, it's possible to upgrade the USB port - otherwise, you may be better off using the 12V port (cigarette lighter) since you have wireless CarPlay available to you.
In my Fusion, I'm stuck using wired Android Auto, so I am unfortunately not able to use the 12V port for charging.
You can get an adapter to change that wired android auto to wireless. I've done this in my ute. Then with my s22 I can use the 12v port with a QC3.0 compatible charger and get above 1% per minute charge whilst still having android auto running.
The adapter plugs in to the USB port for android auto and then offers up a wireless connection. Everything is automatic once set up.
Slow charging though... that seems orthogonal?