  We construct $s$-interleaved linearized Reed--Solomon (ILRS) codes and
variants and propose efficient decoding schemes that can correct errors beyond
the unique decoding radius in the sum-rank metric. The proposed
interpolation-based scheme for ILRS codes can be used as a list decoder or as a
probabilistic unique decoder that corrects errors of sum-rank up to
$t\leq\frac{s}{s+1}(n-k)$, where $s$ is the interleaving order, $n$ the length
and $k$ the dimension of the code. Upper bounds on the list size and the
decoding failure probability are given where the latter is based on a novel
Loidreau--Overbeck-like decoder for ILRS codes. We show how the proposed
decoding schemes can be used to decode errors beyond the unique decoding radius
in the skew metric by using an isometry between the sum-rank metric and the
skew metric.
  We generalize fast minimal approximant basis interpolation techniques to
obtain efficient decoding schemes for ILRS codes (and variants) with
subquadratic complexity in the code length.
  Up to our knowledge, the presented decoding schemes are the first being able
to correct errors beyond the unique decoding region in the sum-rank and skew
metric. The performance of the proposed decoding schemes and the tightness of
the upper bound on the decoding failure probability are validated via Monte
Carlo simulations.
