Some of the Church Fathers bore witness in their writings to the Jewish view of Susanna. These Church Fathers lived in the early to mid Amoraic period and personally knew some of the sages and often came to them with questions about scripture and Judaism in general.
Origen wrote in his Letter to Africanus:
"...And I make it my endeavour not to be ignorant of their [the Jews'] various readings, lest in my controversies with the Jews I should quote to them what is not found in their copies, and that I may make some use of what is found there, even although it should not be in our Scriptures. For if we are so prepared for them in our discussions, they will not, as is their manner, scornfully laugh at Gentile believers for their ignorance of the true reading as they have them. So far as to the History of Susanna not being found in the Hebrew [the Jewish scriptures]...Moreover, I remember hearing from a learned Hebrew, said among themselves to be the son of a wise man, and to have been specially trained to succeed his father, with whom I had intercourse on many subjects, the names of these elders, just as if he did not reject the History of Susanna, as they occur in Jeremias as follows: The Lord make you like Zedekias and Achiab, whom the king of Babylon roasted in the fire, for the iniquity they did in Israel...And I knew another Hebrew, who told about these elders such traditions as the following: that they pretended to the Jews in captivity..."
We find that Jews in the time of Origen were familiar with the story of Susanna, and some even had a tradition that the two judges in the story were actually Tzidkiyahu ben Ma'asiyahu and Achav ben Koliyah (Yirmiyahu 29:21). Ever-zealous to the Christian faith, Origen then proceeds to invent a reason as to why that story isn't included in Daniel. According to him, the Jewish sages removed it in order to not smear the names of the Jewish elders.
However, another Church Father, Jerome, in his commentary on Yirmiyahu, gave the real reason as he heard it from the sages of his time (emphasis mine):
"The Hebrews say that these men who "committed foolishness in Israel" and "committed adultery with the wives of their fellow citizens" are the elders to whom Daniel spoke...But what is said in the present passage, "whom the king of Babylon roasted in the fire," appears to contradict the historia of Daniel, which asserts that the elders were stoned to death by the people as a result of Daniel's judgement, whereas here it is written that the king of Babylon roasted them in the fire. For this reason, this story is rejected as a mere fable by many of us and by almost all of the Hebrews; nor do they read it in their synagogues. "For how could it be," it is argued, "that captives had the authority to stone their own leaders and prophets?"
Interestingly, though, the story wasn't entirely rejected in later generations:
Rabbi Avraham Zacuto wrote in Sefer Yochasin:
"...דניאל בשנת תר"ס התחיל כשנחרב בית המקדש. ואז בגלות בבל היתה המעשה שושנה בת חלקיה אשת יויקים והיתה יפה מאוד...ואז דניאל בחכמתו ובנבואה הצילה...ואז הרגו לזקנים. ואולי היה זה לאחאב בן קוליה וצדקיה בן מעשיה שקלם מלך בבל באש..."
Translation: "...Daniel in the year 660 started out when the Temple was destroyed. And then in the Babylonian Exile happened the Tale of Shoshanna, daughter of Chilkiyah wife of Yoyakim, and she was very beautiful...and then Daniel in his wisdom and prophecy saved her...and they killed the two elders...and perhaps this was Achav ben Koliyah and Tzidkiyah ben Ma'asiyah who were burned in fire by the king of Babylon..."
Rabbi Gedalyah Ibn Yechiyah similarly wrote in Shalshelet Hakabbalah:
"...וראיתי בספר יוחסין...אחר זה היה מעשה שושנה בת חלקיה אשת יהויקים שרצו שתי זקנים שופטים לאונסה וגזמו אותה שאם לא תשמע אליהם שיעידו נגדה ששכב' עם בחור אחד. והיא לא רצתה ודניאל בחכמתו הצילה. וי"א שאלו הזקנים היו אחאב בן קוליה וצדקיה בן מעשיה נביאי השקר..."
Translation: "...and I saw in Sefer Yochasin...after this was the Tale of Shoshanna daughter of Chilkiyah wife of Yehoyakim that two elder judges wanted to rape her and threatened her that if she wouldn't listen to them, they would bear witness against her and claim that she lay with a young man. And she didn't want to and Daniel in his wisdom saved her. And some say that these elders were the false prophets Achav ben Koliyah and Tzidkiyah ben Ma'asiyah..."
And Nachmanides was familiar with a "Scroll of Shushan", which is commonly understood today to referring to a scroll containing Susannah along with other apocryphal works (Devarim 21:14):
"...It is also commonly used in the Aramaic language, as is written in the Scroll of Susanna: “And the king of Assyria sent to all amira (servants) of Nineveh and to all d’amrin (who serve) on the sea coast, and to the servant of Carmel and Gilead [to come with him to the war], but all the servants of the land disregarded the commandment of Nebuchadnezzar and they were not afraid of him.”"
In short, it seems that this story was thought by some to be pure fiction, while others thought it had certain merit to it, but more as an extra-biblical midrash-like tradition, not on par in terms of holiness with scripture.
A note on the other additions:
It's pointed out by Daat that there's a midrash similar to the prayer of Azaryah and his friends:
"Ḥizkiya clarifies his previous statement: Their descent is mentioned in this hallel, as it is written: “Not to us, God, not to us,” a verse that Hananiah recited. Mishael recited: “But to Your name give glory.” Azariah recited: “For Your mercy and for Your truth’s sake.” They all recited together: “Why should the nations say: Where now is their God?” This hallel also alludes to the ascent of Hananiah, Mishael, and Azariah from the fiery furnace, as it is written: “Praise the Lord, all you nations, laud Him all you peoples. For His mercy is great toward us, and the truth of the Lord endures forever, halleluya” (Psalms 117). Hananiah recited: “Praise the Lord, all you nations,” for the overt miracle performed for them before the nations. Mishael recited: “Laud Him all you peoples.” Azariah recited: “For His mercy is great toward us.” They all recited together: “And the truth of the Lord endures forever, halleluya.”" (Pesachim 118a, Shemot Rabbah 9:1 and Tanchuma Noach 10)
Similarly, a parallel midrash for Bel and the Dragon is brought in Beresheet Rabbah 68:13 (my translation):
"And I will deal with Bel in Babylon, And make him disgorge what he has swallowed" - for Nevuchadnetzar had a dragon and would swallow anything that was thrown before it. Said Nevuchadnetzar to Daniel: "How great is its strength that it is able to swallow anything thrown at it?" Answered Daniel: "Give me permission and I shall weaken it." He permitted it. What did Daniel do? He took hay and mixed in it nails which pierced its intestines, as it is said: "And [I will] make him disgorge what he has swallowed."
For this, it seems to me that these stories were known by the Jews - but they also knew that they weren't actually written prophetically by the Men of the Great Assembly, those who authored Daniel. Therefore, these later additions seem to have been embellishments of these earlier traditions.
