It's... complicated. The title of first digital computer can be argued to be ABC, Z3, Colossus, or ENIAC, and which one you give it to is going to be decided on the basis of how precisely you define "first digital computer." Given that there is also an element of nationalism to the decision (is the first computer German, British, or American?), it's not entirely unreasonable to suppose that the criteria is partially determined by the desire of whom to crown.
Personally, I don't think the fact that the Z3 and the Colossus were discovered to be Turing-complete long after they were last used should really qualify them for a title based on "first Turing-complete machine." The long time it took to establish Turing-completeness indicates that they weren't designed to be Turing-complete, and that they are is more a reflection of just how low a bar it is to be Turing-complete than the capabilities of the machines themselves. In other words, I would submit that the phrase "first Turing-complete machine" should really be understood as "first intentionally Turing-complete machine."
Another framework that makes sense to understand is the role that the computers had on later development of the field. ENIAC clearly has a massive influence, since it's the one that spawned more recognizable computers as its progeny. The influence of ABC on ENIAC only came out much later (and is still somewhat debated). Z3 had little impact on the field later because it was on the wrong side of WW2. Colossus I believe did influence the Manchester machines, but this link was not known at the time because of the secrecy around Colossus.
Personally, I don't think the fact that the Z3 and the Colossus were discovered to be Turing-complete long after they were last used should really qualify them for a title based on "first Turing-complete machine." The long time it took to establish Turing-completeness indicates that they weren't designed to be Turing-complete, and that they are is more a reflection of just how low a bar it is to be Turing-complete than the capabilities of the machines themselves. In other words, I would submit that the phrase "first Turing-complete machine" should really be understood as "first intentionally Turing-complete machine."
Another framework that makes sense to understand is the role that the computers had on later development of the field. ENIAC clearly has a massive influence, since it's the one that spawned more recognizable computers as its progeny. The influence of ABC on ENIAC only came out much later (and is still somewhat debated). Z3 had little impact on the field later because it was on the wrong side of WW2. Colossus I believe did influence the Manchester machines, but this link was not known at the time because of the secrecy around Colossus.