I mean what you are describing sounds like an exact match for oscilloscope current probes : https://www.digikey.com/en/articles/understanding-selecting-effectively-using-current-probes They are expensive, but convert AC and DC current to a voltage range reasonable for a scope and do so in an isolated manner. Bandwidth is basically as much as you are willing to pay for.

For current shunts there is the EEVblog uCurrent but it’s not isolated, just a very low burden voltage shunt and amplifier essentially> https://www.eevblog.com/projects/ucurrent/

I know it may seem obvious, but did you check the pins of the BOOT0 switch itself and the nearby capacitor? A stray bit of solder there could cause the switch to appear always held down by shorting either the cap or the switch. It doesn’t appear that the boot0 line goes anywhere other than there and the main microcontroller so the issue is likely there.