Early game still favors slaves because it is +20% minerals and food for enslaving right off the bat, no tech required. Robots are +10% minerals, Droids are +15%, and Synthetics are +20%.

The Slave Processing Facility requires Neural Implants tech, which only needs Genome Mapping. The tech will fire at a very high rate if you're a slaving empire (1.25 for collectivists, 2.0 for having any slaves). It can literally be the second society tech you research, and it will add +15% more to slave minerals and food output. This will cost a total of 840 base research.

Neural Implants tech is also the only prerequisite for Stimulant Diet, the stacking +10% output from slaves repeating tech. 1500 base, 2340 all together.

Droids tech requires Colonial Centralization, Robotic Workers, Planetary Unification, and Powered Exoskeletons. Total of 2,460 base research.

For slightly less total research spent you can get slaves with +45% mineral output, even without a single mineral related species trait. The droids will give +15%, and every boost available to them via policies is also available to the slaves. Not only will they be getting more out of the mines, but they'll require much less support than free populations because of the massive food output boost. Two farms, a power plant off world to drive the farms, 23/26 = 88% tile efficiency, right there with the mixed free/robot option and getting far more minerals out of the deal. Plus they'll breed themselves out to fill the planet and won't require the up front outlay the robots do.

Slavery is way too good at the mineral game. If it was up to me robots would get more boosts, and at least a building to give them the same sort of boost the slave processing facility provides. And maybe some kind of robot factory that can slowly grow robot pops with a mineral maintenance cost or something.