I guess (based on what I have seen in mbed and Arduinoi LIB code):
this USB-A connector is only supported as Host (not Device). So, a USB stick there should work (as an MSD host device, called also MSC, MDM?).
The UART on USB-C is a different interface, you should not lose it. Except: you would try to use USB-C connection as USB Host Memory. But I think it is anyway not possible because on USB-C the USB power for the memory stick is not provided.
I assume as well: even you implement the USB-A as USB Memory Host (there should be some code, e.g. PluggableUSB, PluggableUSBMSD, USBMSD) - you need also FatFS:
if you want to read and write files on USB memory stick - you need the the file system. The MSD device comes as SCSI controller (providing SCSI device commands). Your file system has to be bound to this USB device (and use the SCSI command for file and directory handling).