Why do you need a transceiver for bitbanging USB? Simply toggle the pins?
A 48MHz mcu will not be able to sustain 12Mbps even in your best dreams (Exception: Pi Pico, handling USB with PIO).
So, your only option will be USB 1.0 spec @ 1.5Mbps, at best.
You have several usb projects doing this:
https://github.com/IOsetting/py32f0-template/issues/12
a trouble with STM32 is that i've not figure out an 'easy' way to toggle 'complementary' differential signals. the timers can do it but that it isn't quite like transmitting a data stream.
a trouble with usb is that it isn't 'pure differential' as there are additional signals such as 'single ended zero' i.e. both D+ and D- at GND.
so that adds a little more 'complications'
sustaining 12 Mbps with SPI or even higher speeds like 20 Mbps or even higher is feasible. I've tried updating data in a spi flash chip of the Windbond W25Q64BVSIG type SPI flash ram and has been able to do that quite stably at 20 mhz off a stm32f103c8 device.
there is actually an (old) chip that does it well USB1T11A
https://www.onsemi.com/products/interfaces/wired-transceivers-modems/usb1t11ahttps://www.onsemi.com/download/data-sheet/pdf/usb1t11a-d.pdfit is 'made for purpose' - a usb 1.1 full speed transceiver
it perfectly fit the 'SPI' interfacing option.
apparently while this is marked 'obselete', it is apparently still 'widely' in use
https://www.lcsc.com/product-detail/span-style-background-color-ff0-USB-span-ICs_onsemi-USB1T11AMX_C464142.htmlit is 'made for purpose', just that in the 'online flea markets' these days
https://www.aliexpress.com/w/wholesale-USB1T11A.htmlthis 'old chip' practically cost as much as many microcontrollers itself in the 'retail' small quantities markets.
it may still be worth getting though, as practically the large set of the stm32g03x series practically don't have usb, even if some of them have more sram and flash.
another way which is 'common;' is to simply patch a usb-uart chip, e.g. CH340
at 'retail' quantities, a CH340 completely built with a crystal, LDO, usb connector, a 5v, 3v switch, accessories components (smd caps, resistors) + PCB + header soldered can be about 'equal' in price to a single piece of USB1T11A
https://www.aliexpress.com/item/1005004824108230.htmlhttps://www.aliexpress.com/item/1005005272826903.htmlbut of course with a USB1T11A, one is not limited to 'usb serial', one can practically 'bit bang' any USB protocol e.g. HID and make a keybboard, mouse etc
the other thing is there are probably 'other' chips which bundle a usb function on chip but is probably not in the stm32g03x series.
e.g. stm32f103c8, cost a little more but is probably what it cost to add that usb functionality.