We learn from quantum mechanics courses that one recovers classical mechanics in the limit when Planck's constant goes to zero. This can be seen in the path integral formulation. This is why macroscopic objects mostly obey laws of classical mechanics and that quantum effects are only seen at small scales.
The claim that quantum theory tends to classical physics in the limit $\hbar\to 0$ is common, but it is false if quantum mechanics is an accurate description of how reality works. Even an object the size of Saturn's moon Hyperion would undergo quantum interference on large enough timescales (about one month) if it was isolated from interactions with all external systems:
https://arxiv.org/abs/quant-ph/9802054
https://arxiv.org/abs/quant-ph/0605249
This would happen regardless of the fact that $\hbar$ is small compared to macroscopic quantities in the same units. But if a system interacts with external systems to produce a record of the interfering observables, then interference is suppressed: this effect is called decoherence. Decoherence causes the world to look classical, not the size of $\hbar$.For For a review see
https://arxiv.org/abs/1911.06282
For a path integral based approach see
https://arxiv.org/abs/quant-ph/0208026
Another problem with your question is that since $\hbar$ has units, you can change its numerical value to whatever non-zero value you want. As for a world in which it is close to zero on scales we are interested in, that looks like the world we live in now. Some observables evolve in a more or-or-less classical way that looks a like a collection of parallel universes on the scales of everyday life:
https://arxiv.org/abs/quant-ph/0104033
https://arxiv.org/abs/1111.2189
This means you have to do precise experiments to see effects like quantum interference or entanglement, although even macroscopic objects carry locally inaccessible quantum information:
