UART speeds up to 921600 baud worked reliably for me in similar settings.
Depending on the chip series you might redirect printf to SWO which can be even faster than that.
Use a high resolution timestamp (extra timer or DWT cycle counter avail. on some cores) for timestamping you logs.
You may also set aside a larger text (char) buffer in RAM and log to RAM (sprintf) with very little overhead and inspect/dump the RAM buffer later.
Might combine this with setting breakpoints at some critical points in the code and inspect the RAM buffer then.
If you have spare pins, you might add a logic analyzer (LA) and set some pins aside for signalling certain states of the connection.
There are SW tools that act like a software LA using a RAM buffer technique. Search for TraceX or https://gitlab.com/KnarfB/timedoctor.
A host side tool like wireshark may capture USB data on the wire.
Add assertions to your code to catch design flaws early.
hth
KnarfB
