You’re right, automation isn’t why housing and education are more expensive now. The increase of those is direct result of government policy choices encouraged by the voters. For housing, were taking zoning laws, and public objection laws. Higher education tuition increases for public universities is directly tied to cuts in government support for said government institutions.
But let’s get back to the topic at hand, whether or not benefits of productivity increases are felt by workers, or if it’s primarily concentrated with the already wealthy.
The answer is clear. The benefits are concentrated with the few. Sure prices drop, but so do wages and overall wealth by the majority. This isn’t even a controversial take. Government statistics have been tracking this for 40 years.
You’re asking questions like they’re some great unknowable, but not only is this common knowledge, but just an google image search away.