This is a very complicated question and I think the answer would depend on the particular time period, location, and work of the Old/New Testament that we're talking about. In general, I would say that to the extent that biblical works refer to real-world events, they do so because those events were important to their readership and the works expect the readership to be familiar with those events on at least some level (even if the works put their own unique "spins" on the events), but not necessarily intimately familiar with them. The biblical works weren't intended to be strictly historical in nature but instead to impart some religious lesson, and so I think it's fair to assume that their historical accuracy varies by biblical work, by event, and frankly by the abilities of the authors and the degrees to which they wanted to be historically faithful. In other words, biblical works can be helpful as potential historical sources but you would certainly want to compare them to other types of evidence and not take them as the "gospel" truth about a particular event. I haven't looked into these issues in a long time, but from my recollection -

The story of Exodus continues to be debated to this day (whether there were any Jewish slaves expelled from Egypt and, if so, how large the expulsion actually was).

The Books of Maccabees are thought to be reasonably useful sources for insights into the Maccabean revolt against the Seleucids (or at least among the best narratives that survive), but I don't know how they compare to the complete universe of sources/archaeological materials.

The Pharisees and Sadducees were real schools of Jewish religious thought that would have been active during Jesus's life (together with another group, the Essenes), though we lack complete information about the composition, views, and roles of those groups.

The author identified as Luke's placement of Jesus's birth during a census conducted by an official named Quirinus, and the description of the census itself, is problematic and probably mistaken in a few respects. The author claims that the census was declared by Augustus, was empire-wide, took place when Quirinus governed Syria and when Herod ruled Judea, and required people to travel to their home towns in order to be counted. Except that - Augustus never ordered an empire-wide census, Quirinus governed Syria several years after Herod died, and, so far as we know, censuses never required people to travel to their home towns (the primary purpose of a census was for tax collection; it didn't do the empire any good to force you to go back to your home town to be counted - they needed to know where you would be living when the tax collectors showed up, not where you had come from).