I'm a bit surprised "SMU" has not been mentioned here yet:
But it probably also does not matter much because of budget constraints
https://www.ebay.com/sch/i.html?_nkw=keithley%20smuWould this be hard to buy / build?
From: 0-10V - 0-1A
Step: 100uV / 10uA
Have you thought about how realistic those values are?
What sort of cables do you want to need if you want to keep a 5V supply within 100uV over a 0 to 1A current differential?
That's a voltage resolution of 1:100000
Have you thought about how you want to adjust such a thing? That is definately not going to work with a 10 turn potentiometer.
Things like these are very expensive, but most of the price does (probably) not go into the components, but in the engineering such things for a small market. But also because they are only made by companies who do not care about price, but only about qualtity and robustness.
As a hobbyist it is fairly doable to slap a few DAC's onto a microcontroller, add a display, some rotary encoders and some opamps for the output section.
Opamps don't deliver much current. One easy option is to add a buffer such as LME49600 (can these be parralelled?) Or on a low budget maybe even some integrated audio amplifier.
For a DAC you could for example take an MCP4922. It's only 12 bit, but in the datasheet the've shown a simple trick to increase it's resolution.
You can get more (absolute) accuracy by carefull calibration, or by using a good adc and fine adjustment in a software loop.
Fairly good ADC's have become pretty affordable. For example take a look at ADS1220, or other DAC's in that series.
Do you only want to measure current, or do you also want a current limit to work reliably at your resolution?
It might be a better idea to build and adjustable current source.
For measuring current, you can buy expensive high accuracy & stability resistors, But you can also use a cheap power resistor and callibrate it yourself. You can also for example glue a thermometer to it and after characterisation of the resistance deviation, you can partly compensate for it in software.
How good you can build something like that and what accuracy / resolution / reliability you get will mostly be dependant on the experience you have with electronics and the amount of time you put into it.
But with a reasonable amount of effort you will probably:
1). Get much better accuracy / resolution than your KORAD.
2). Have built designed something to be proud of, and have lots of fun in the process.
3). Learned a lot about electronics.
4). Have a usefull device for doing experiments.