  Tensor network methods are powerful and efficient tools to study the
properties and dynamics of statistical and quantum systems, in particular in
one and two dimensions. In recent years, these methods were applied to lattice
gauge theories, yet these theories remain a challenge in $(2+1)$ dimensions. In
this article, we present a new (decorated) tensor network algorithm, in which
the tensors encode the lattice gauge amplitude expressed in the fusion basis.
  This has several advantages: Firstly, the fusion basis does diagonalize
operators measuring the magnetic fluxes and electric charges associated to a
hierarchical set of regions. The algorithm allows therefore a direct access to
these observables. Secondly the fusion basis is, as opposed to the previously
employed spin network basis, stable under coarse graining. Thirdly, due to the
hierarchical structure of the fusion basis, the algorithm does implement
predefined disentangles, that remove short-scale entanglement.
  We apply this new algorithm to lattice gauge theories defined for the quantum
group $\text{SU}(2)_{\rm k}$ and identify a weak and a strong coupling phase
for various levels $\rm k$. As we increase the level $\rm k$, the critical
coupling $g_c$ decreases linearly, suggesting the absence of a deconfining
phase for the continuous group $\text{SU}(2)$. Moreover, we illustrate the
scaling behaviour of the Wilson loops in the two phases.
