DIY Android Auto Power Booster
As I understand the OP wants to use some standard USB port from car equipment to communicate with a smartphone, but provide an alternative power source (5V 2.4A) to boost smartphone charging functionality. This function (boost) was frequently achieved with "Y-cables", which were used to connect external USB-HDD enclosures in the past. One of Y-end would contain D+/D- data lines, and the other Y-end holds just GND and VBUS. 



So this kind of cable should work for a smartphone, except that the phone has Type-C connector. Unfortunately, on a quick search on Google I wasn't able to find the exact configuration, but it should be possible to make such cable with some effort and luck.

First, if you take a standard USB A to USB-C cable (preferably a thick one, with imprinted text "AWG24/AWG28" on cable) and carefully open it up near type-A end, you can cut red wire, and re-connect it to another piece of cable with Type-A plug. The ground wire should be split between two Type0A plug cables. The original Type-A plug (with no VBUS) should go to the USB car port (for data transfer), and the attached extra (Y) end would go to the 2.4 A charger, just as your diagram indicates (except that grounds have to be connected). This should be done without any "breakout boards", they are bad. Also, before doing this you need to check if the grounds between your boost charger and ground on USB port are either not connected, or connected to each other with no significant potential difference, otherwise the entire project will fail.

Unfortunately, a standard good Type-A-C cable would have 56k pull-up on CC pin. So yes, you need to worry very much about the 56k pull-up. The 56k pull-up would make the smartphone to draw only 500 mA for charging, so you will have no "boost". To have the boost, the Type-C end should have 10 k pull-up, so the phone would be informed to draw full charge. Therefore, for this kind of project you will need to find an "illegal" USB-A to USB-C cable, with 10k (or 22k) pull-up on CC line, opposite to the ones recommended by "Google engineer Benson Leung", the "bad" ones. Unfortunately, this pull-up resistor is mounted inside Type-C overmold. One other way is to open the overmold carefully, and change the resistor, the task which will require some dexterity.

Alternatively you can use the pictured above Y-cable and replace the common Type-A end with Type-C DIY connector like this one, with proper value of pull-up resistor. This would be the best and neat variant.

ADDITION: This Y-cable with Type-C should work if it has 10k (or 22k) pull-up.