Unfortunately, the question cannot be answered unambiguously:, it depends on the connection in the car:
In some cases, the USB connections in cars are intended for the operation of USB data sticks (MP3 music) - in this case, if at all, charging the mobile phone via USB does not work at full speed because the current supplied by the connection is not sufficient for this. It is also possible that - also depending on the USB connection installed in the vehicle - the playback of music from the mobile phone is not possible.
With the selected adapter, a cable with a USB-C connection on both sides must also be used so that it works with the connection on the mobile phone - this often leads to contact problems.
My suggestion would be to use a USB-A to USB-C cable instead (e.g.
https://www.digitec.ch/de/s1/product/roline-usb-31-gen2-kabel-a-c-050m-31-usb-kabel-5639006) - it costs half as much and at least avoids the problems of multiple connections.
Otherwise, such a cable can be combined with a USB car adapter (e.g.
2GO Power Set - on-board socket is often also available in non-smoking cars, check beforehand!) - then at least recharging in the car should work.
For the audio connection (if this does not work via USB or the solution with the separate power supply is chosen), Bluetooth is then an option (if the car radio can do this) or possibly also a coupling via a second cable with two 3.5 mm jack plugs - if the mobile phone and car radio have this.