This is a follow-up question to this one. Consider $R=k[x,y,z]$ with an action of the symmetric group $S_3$ by exchanging variables $s:x\rightleftarrows y$ and $t: t \rightleftarrows z$. Define the $R$-$R$-bimodule $R_s = R⊗_{R^s} R$ for $R^s=[x+y, xy, z]$ the invariants under $s$, and similarly define $R_t$.
Claim: in Example 2.9, this lecture claims that the bimodule $R⊗_{R^s} R⊗_{R^t} R⊗_{R^s} R$ decomposes into indecomposable bimodules as
$$ \bigl(R⊗_{R^{s,t}} R\bigr) ⊕ \bigr(R⊗_{R^t} R\bigr).$$
Question: I know that for arbitrary Coxeter groups, it is cumbersome to find indecomposable Soergel bimodules. However, for $S_3$, there should be some easy argument, shouldn't it? How can this claim be easily justified?