Drizzle intensity is determined by visibility just like snow.
1/4sm or less is +DZ. DZ is >1/4sm and <=1/2sm. -DZ is >1/2sm.
But yeah you never really see it in obs except for some stray AWOS sites. Usually the vis reduction gets attributed to fog so in ASOS METARs you see -DZ FG.
I’ll assume the forecast algorithms just see the visibility forcecast with the drizzle forecast and if there’s 1/4sm in the grids “heavy drizzle” gets regurgitated in the wording.