The promote_rule with an Irrational{s} type and a Complex{Irrational{s}} type (where s is the same Symbol) gives a StackOverflowError. The intended type is probably Complex{Irrational{s}}, as demonstrated by swapping the arguments:

If the parameters are different (e.g. Irrational{:ℯ} with Complex{Irrational{:π}}), then there is no issue as it promotes to ComplexF64.

Julia version 1.9.2 installed on Windows 11 with the Julia installer https://julialang.org/downloads/