  We establish a cluster theoretical interpretation of the isomorphisms of
[F.-H.-O.-O., J. Reine Angew. Math., 2022] among quantum Grothendieck rings of
representations of quantum loop algebras. Consequently, we obtain a
quantization of the monoidal categorification theorem of
[Kashiwara-Kim-Oh-Park, arXiv:2103.10067]. We establish applications of these
new ingredients. First we solve long-standing problems for any non-simply-laced
quantum loop algebras: the positivity of $(q,t)$-characters of all simple
modules, and the analog of Kazhdan-Lusztig conjecture for all reachable modules
(in the cluster monoidal categorification). We also establish the conjectural
quantum $T$-systems for the $(q,t)$-characters of Kirillov-Reshetikhin modules.
Eventually, we show that our isomorphisms arise from explicit birational
transformations of variables, which we call substitution formulas. This reveals
new non-trivial relations among $(q, t)$-characters of simple modules.
