2 -representations of small quotients of Soergel bimodules in infinite types

We determine for which Coxeter types the associated small quotient of the 2-category of Soergel bimodules is finitary and, for such a small quotient, classify the simple transitive 2-representations (sometimes under the additional assumption of gradability). We also describe the underlying categories of the simple transitive 2-representations. For the small quotients of general Coxeter types, we give a description for the cell 2-representations.