My understanding of trickle down economy, could be incorrect, has been that it is a policy that advocates govt. giving money to the rich. Through tax breaks and other means. The idea being that the rich would then spend that money in ways that would allow the benefits to trickle down to the poor.

This is correct. The idea is that money spent by the wealthy enjoying themselves or making themselves wealthier through investments eventually reaches the poorest - in some form.

Quite why we've persuaded ourselves we need to do this through a remote & deaf middleman is anyone's guess, when governments we elect could just direct money through policies we can all argue about and nudge in our own small ways.