Why does the Septuagint Bible consist of additional books (3 Kings, 4 kings, Maccabees,etc.) and psalms (151,152)? From my understanding some of these books and psalms were found in the DSS, so why wasn’t it included in the canon?
The question of what the content of the Septuagint is/was is not an easy one. A number of Hebrew documents were translated into Greek in Alexandria in the 3rd century BC. These documents became known as the Septuagint. Having said that, a number of non-canonical writings were also translated into Greek at an early date, but after the third century, and besides this, a number of documents were written by Jews which were originally in Greek. The exact list of works which are included in the "Septuagint" is, therefore, impossible to list with complete confidence. We do not have manuscripts of the Septuagint old enough to settle the question of what was in the Greek Old Testament at any one date with certainty. Besides, the canon of the Old Testament may have been somewhat fluid in the second century BC.
Adding to the problem is the fact that the early Christian Church began to use texts such as 1st Maccabees, Wisdom, Ecclesiasticus and others in the second and third century. Whether these were part of the "Septuagint" at that time is probably debatable. What is not debatable is that many Christians included them in their list of authorized works.
It was the Jews, not the Christians, who eventually excluded what is now known as the Apocrypha as well as other works, such as those in the pseudepigrapha. This can be confusing. For example, 3 Esdras is a work which was around at that time, but it was never considered as part of the OT canon by the church or the Jews, but it was used by some anyway. Here is the bottom line for me. I believe, on faith, but also on the evidence for inspiration, that God entrusted to the Jews what would be selected by consensus as part of the authorized canon of the Old Testament. They definitely rejected 1 and 2 Macabbees, Tobit, Judith, 1,2,3 and 4 Esdras, and all books outside the 39 books we now accept as our Old Testament. The fact that some in the Christian Church considered all or part of the Apocrypha as inspired or sub-inspired does not affect my opinion about what we can accept with confidence as authoritative is not particularly significant to me.
On a small side note, I believe that 3rd Kings and 4th Kings you refer to is actually 1 and 2 Chronicles ,and they are therefore part of the OT canon. For your information, what is known as Psalm 151 was found in the Dead Sea Scrolls, in Hebrew. Psalm 152 was not. Neither of these psalms is in the accepted authorized Jewish OT, so I would not include them–not that the inclusion or exclusion of these two psalms would be particularly significant to Christian teaching. It is probably not worth debating the inclusion or exclusion of Psalm 151. This is a debatable one. The DSS did include a few fragments of Sirach (in Aramaic) and of Tobit.