Do we ever see the overload setting post-TOS?
Nope. The perfect time to threaten with that would be in "Frame of Mind", but instead the crazed Riker threatens to use Level 16 to, well, level the building...
Also re: the bum killing himself in COTEOF...I always assumed he set it to overload and then fired it. Reason being the sound effect, and that he doesn't seem to be aiming it at himself.
Makes at least some sense. Supposedly, the controls are difficult to operate correctly - leading to the demise of not just the bum, but Nona in "A Private Little War" as well.
I mean, yeah, the latter could be due to there simply being a safety of some sort for these weapons. But we have seen all sorts of people expertly or at least inexpertly operate captured Phaser One and Two units, so a complex fumble rather than a simple inability to release the safety is a likely cause of death...