If you take any capacitor and charge it, it'll take quite some time to discharge on its own.
The discharge is usually controlled by a resistor in parallel with the capacitor on the PCB. Removing the capacitor from the board disconnects it from the discharge resistor. So not much "modern electronics" going on here :-P
Note: do NOT do this with thin wires and large capacitors / arrays of capacitors, or you may get a hot copper shower.
Putting the leads over a capacitor, the multimeter will show the voltage and discharges the capacitor with a constant safe current. Beeps can be used to indicate when the capacitor is safe to handle or not.
That's all that I use. Don't hold the resistor in your hand though, depending on the size of the capacitor they can get quite hot. I usually use some pliers to hold the resistor.
"Shawnee teenager is electrocuted while working on a computer":
https://www.kctv5.com/story/19767067/teen-electrocuted-while...
Same story as above as link not available:
https://www.dailymail.co.uk/news/article-2215200/Teenager-Sh...
And a warning:
"I just received an electric shock from an unplugged computer"
https://www.reddit.com/r/computers/comments/53cio2/i_just_re...
[edit] Ah I see this is called a bleed resistor, never mind