It's the power requirements that boggle my mind more than anything else.
The Warp Core in the Enterprise's engine I can accept - it's good and BIG and engine-roomy

.
But a power source that's the size of a big battery that can be used in a hand held energy-weapon is harder to take on.
Because of the existence of the Replicator's and the Transporter it has always been clear that in the Star Trek universe we have conquered the matter-energy-energy-matter conversion that is the gateway to so much. It's actually one of the things I've always had to 'ignore' in the series' as if you can do that, you can pretty much do anything.
But leaving that aside, then how you power a phaser is clearly done with matter-energy conversion rather than matter-anti-matter annihilation.
"Clearly" of course comes with the proviso that ... Dammit Jim! I'm an economist, a historian and an engineer, not a theoretical physicist! :lol:.