Gregory E. Sterling, Shaping the Past to Define the Present: Luke-Acts and Apologetic Historiography (Wm. B. Eerdmans Publishing Co., 2023), 96:
Josephus was not the only Jewish author to note the incompleteness of the LXX. The Jewish-Christian author who composed Luke-Acts also thought that the LXX was incomplete in the form in which it circulated. It may relate the story of Israel’s past, but not of the present. For that reason, Luke elected to write a continuation of the LXX. Unlike Josephus, who rewrote the entire story of Israel, this Christian author elected to continue the story without rewriting the earlier scrolls. This is a good example of “conceptual integration” or “blending”…in the historiographical tradition. The author did not, however, do this de novo: there were precedents for this undertaking in the historians who attempted to continue the work of their predecessors.
The Amateur Exegete 