I found a great solution to the charging problem when using wired CarPlay in my 2021 Prime SE. The power output from the CarPlay USB port is so low my iPhone barely charges at all when in use. I experimented with an aftermarket wireless CarPlay adapter. This allowed me to fast charge my phone using the cigarette lighter adapter, but the wireless CarPlay was buggy, slow, delayed, prone to dropping its connection, and had poor audio quality.
I have been using this USB-C PD power splitter from Tindie and it works great. I get the reliability of wired CarPlay along with fast charging capability. One port plugs into the CarPlay USB port while the other plugs into a USB fast charger in the cigarette lighter adapter. Then a single USB-C to lightning cable charges my iPhone.
USB-C PD power splitter from Essence Engineering on Tindie
I have been using this USB-C PD power splitter from Tindie and it works great. I get the reliability of wired CarPlay along with fast charging capability. One port plugs into the CarPlay USB port while the other plugs into a USB fast charger in the cigarette lighter adapter. Then a single USB-C to lightning cable charges my iPhone.
USB-C PD power splitter from Essence Engineering on Tindie