With the meter, you can see a current peak up to a nice round value, followed by a voltage drop. The low refresh rate makes it not nearly as clear as with an oscilloscope, but once you know what to look for, it is easy enough to pick up. (And if you really want to, you can get one with a breakout to connect scope probes).
If this is an issue you run into often, I'd also suggest a usb variable load tester to check exactly how much current a port will output.
1) The battery is dead and cannot be charged.
2) The cable is a non-charging one or internally damaged/dead or non-fastcharging or with limited fastcharging capability.
3) The charger is not capable enough to supply the max current that the device can use to charge itself.
To troubleshoot the problem, first check the Voltage/Current specs for your device, make sure that the charger plug/battery can provide the same voltage but same or higher amount of current. Then use a USB power meter to see what is actually being drawn (or not) to figure out where and what the problem might be. One key point to note is that for fastcharging all the links in the chain i.e. charger, cable and device should support it.
Another use case was when the battery in my laptop was completely empty, which made it switch to some emergency charging mode that didn't like the normally fine USB-C power supply. I found that it did accept charge from an external battery, so I charged it using that for a while until it booted.
I have a cheap device that costs about 2€ on AliExpress. It is not a cable but a little box.