The real space saver is keeping cards in their original boxes but using vertical dividers instead of stacking games flat. Once you've sleeved everything, those boxes actually compress down pretty well if you're not leaving dead air space inside. Grab some cheap cardboard dividers or even make them from cereal boxes - just arrange them so cards stand upright like files rather than lying flat. This cuts your footprint in half compared to stacking boxes on top of each other.
I'd push back a bit on separating everything into new storage containers. Yeah, it works, but you lose the original box art as reference and end up juggling multiple containers when you actually want to play. Plus you're not really solving the shelf space problem - you're just making it more compact but still taking up vertical room. The divider method keeps your games intact and playable while being genuinely space-efficient.
One more thing that helps: don't sleeve components that don't need it. Player tokens, wooden pieces, money tokens - those are fine unsleeved. Focus the sleeves on cards you're actually handling repeatedly. And if you've got expansions, consolidate them into the base game box where possible instead of keeping separate expansion boxes. That's where most people actually lose space without realizing it.