  $\alpha$-RuCl$_3$, a well-known candidate material for Kitaev quantum spin
liquid, is prone to stacking disorder due to the weak van der Waals bonding
between the honeycomb layers. After a decade of intensive experimental and
theoretical studies, the detailed correlation between stacking degree of
freedom, structure transition, magnetic and thermal transport properties
remains unresolved. In this work, we reveal the effects of a small amount of
stacking disorder inherent even in high quality $\alpha$-RuCl$_3$ crystals.
This small amount of stacking disorder results in the variation of the magnetic
ordering temperature, suppresses the structure transition and thermal
conductivity. Crystals with minimal amount of stacking disorder have a
T$_N>$7.4\,K and exhibit a well-defined structure transition around 140\,K upon
cooling. For those with more stacking faults and a T$_N$ below 7\,K, the
structure transition occurs well below 140\,K upon cooling and is incomplete,
manifested by the diffuse streaks and the coexistence of both high temperature
and low temperature phases down to the lowest measurement temperature. Both
types of crystals exhibit oscillatory field dependent thermal conductivity and
a plateau-like feature in thermal Hall resistivity in the field-induced quantum
spin liquid state. However, $\alpha$-RuCl$_3$ crystals with minimal amount of
stacking disorder have a higher thermal conductivity that pushes the thermal
Hall conductivity to be closer to the half-integer quantized value. These
findings demonstrate a strong correlation between layer stacking, structure
transition, magnetic and thermal transport properties, underscoring the
importance of interlayer coupling in $\alpha$-RuCl$_3$ despite the weak van der
Waals bonding.
