UART is fine if you can find a suitable UART adapter for your PC. Typical cheap suspects go up to around 1Mbaud/s and then start silently corrupting or losing bytes. It needs to be some deluxe USB UART adapter specified for the high datarate you need, with large enough FIFOs so that your OS won't start dropping bytes. They do exist but not necessarily easy to find. This could still prove easiest, compared to implementing USB or Ethernet.
By far, the easiest, i.e. trivial program to get you going is to enable SPI and UART, set up SPI interrupt, and in the ISR, just read the SPI data register and write the content to UART data register; a simple bridge.
Didn't look at STM32U5 datasheet but I'm assuming it's new enough so you can configure the SPI peripheral for full 24-bit data width, so you only get one interrupt per sample. If you enable the FIFO mode in UART (assuming it's available), then you can just write the 3 bytes back-to-back without waiting. This gives very manageable interrupt rate of only 51200 interrupts per second (same as the sample rate).
Interrupt latency (entry + exit) is approximately 20 CPU clock cycles. SPI doesn't need much babysitting, just read the data register, this is maybe 2-3 CPU cycles. Same for writing to UART. It's entirely possible to keep the whole ISR (including overhead) below 50 clock cycles. You have time to spare.
Start simple and go from there.