USB C PD fast power role swap
The STUSB1600A is only a controller that follows now obsolete management of power roles using pull-up/pull-down combinations on CC lines. It doesn't have any PD capabilities. It is very unlikely that it will ever work for your purpose.

The TPS65987D, however, is a PD controller, which can exchange PD serial communication over CC channels. The thing is that by recent PD specifications the only legal way to change power role of a port is using PD communication, so called "Structured VDM", Vendor Defined Messages. By default, power role of a port is in strict relation with data role: UFP is a sink, and DFP is a source. To swap power roles without swapping data roles you need to engage both ends of the Type-C link in PD negotiations.

The thing is that TPS65987 chip is essentially a PD PHY, it can mostly receive and transmit PD messages. The content and interpretation of these messages must be crafted in firmware of some other MCU via I2C ports, although it does look like the TPS65987 has some local messaging capabilities which must be programmed in.

Also be aware that having Type-C connector doesn't automatically imply that the device supports all these fancy PD and power-swap modes, so your target "a smartphone" may not be designed for up to date PD protocol, so expect that the power-up "accessory mode" won't work with all "a smartphones".

All can I say, "good luck".