I’ve looked fairly extensively through the domain‐theory and PL‐semantics literature since Abramsky–Jung ’94 and I have not been able to find a single place where their “adjoint‐pair” version of limit–colimit coincidence has actually been used to do a denotational‐semantics construction that could not equally well have been done with ordinary e-p-pairs. In particular

1. Almost every recursive‐domain construction in the literature still uses chains of embeddings (and projections) and the usual ω‐CPO fixpoint theorem.
2. The places where one does see Scott‐continuous Galois‐connections in the semantics community (most notably in abstract interpretation) exploit them to relate a concrete and an abstract domain, but do not invoke any limit–colimit­-coincidence argument on an ω–chain of such adjunctions. They simply prove ⊔-continuity of the transfer functions (or appeal to widening/narrowing theorems) rather than build a bilimit of adjoint pairs.
3. I know of no papers in programming‐language semantics, game semantics, name‐abstraction models, concurrency semantics, etc., that ever refer back to “the general Scott‐continuous‐adjunction version of Theorem 3.3.7.”

In short, it remains, as Abramsky and Jung themselves said, an elegant but so far unused generalization. Everyone who needs it in practice still falls back on e-p-pairs, and nobody has yet found a semantic construction that genuinely requires the extra generality of non-injective lower‐adjoints.

If you are looking for an application, the only place I can point to is the idea that one could build domains which sometimes “merge” points at later stages (e.g. in some name‐equality or refinement‐of‐abstract‐interpretation story), but nobody has ever carried out that plan in print. So as far as published work goes: no applications have appeared.