Hi,
A custom project might be an option (although this would take longer than buying a ready-made product of course : (
Anyway, if you went the DIY project route, then it's possible to amplify the voltage from a sense resistor, using (say) INA 21x series (an example circuit is attached, to monitor the current flowing where the red arrows are indicated; you could simplify a lot by removing U4 and U9, since they just optionally remove a small offset).
The output at J2 (green arrow) could be monitored with a multimeter, and the circuit could be powered from a battery, since you want everything isolated.
However, for measuring at a higher speed, then the output at the blue arrow could be connected to an ADC board (there are some boards on AliExpress, although it's a bit pricey, but it saves the effort to enter the schematic/create a PCB for that part). And then, something like a Pi Pico Wireless (Pico-W) could be used to send the data to a PC, i.e. PC is isolated, and it would log or chart. The code would be quite simple. If that's a problem, I don't mind helping to write a bit of code, (and I'm sure others would help if there was a major problem, since it's easy for anyone to explore the code if it's on say GitHub).
Also, there's no need to assemble a circuit board for the INA 21x board, since the
eval module is cheap.
A custom PCB would be neater of course, but for a one-off maybe it's all feasible using the ready-made modules approach. I've not done the calculation, but I believe a single sense resistor value should get you several amps of measurement, with mA resolution or better with the above combination of bits and pieces. Others may have better ideas.
EDIT: Just read above that @slugrustle has a DIY suggestion too, using an isolated AMC3301. Neat idea. It looks better than an 'analog linear optocoupler' that I tried in the past, which was disappointing.. I couldn't get decent performance out of it (had noise issues that made low-level measurements not good.).