Just my opinion after reading the Qur'an for 20 years and observing actions and rituals practiced by various sects of Islam.
First, Mohamed would recoil in horror at the phrase "sects of Islam". He thought he was creating a monolith, but after he died men do what men do and started messing with it. IMO, if Mohamed didn't do it or advocate for it, then it isn't part of Islam. The Shia added things like line-of-succession rules and Ashara, and off they went to create an offshoot.
NOTE: Not being a Muslim, I believe the Qur'an was created solely by Mohamed. No god(s) were involved.
1. Abraham religion starts with him, but doesn't end with him, he has branches (Asbat) Quran talked about, linking his family with him.
2. Moses religion starts with him, but doesn't end with him, and Twelve verses have Aaron name along side Moses and 20 verses with Aaron name and while he was a name of God that sails the ship of salvation, he too had twelve branches starting with Aaron and ending with Jesus.
3. Adam religion starts with him, but doesn't end with him, he has Seth (set by God) to succeed him and Noah is the 9th Successor of Adam.
By your logic, the followers of Abraham, Moses, and Adam all innovated when they followed their respective Twelve Successors.
Sorry, this logic doesn't make sense, and the way of the past to way of present to the future is all the same per Quran with no change.
Sunnis are right if Imams (a) are not appointed by God, it would be an innovation. But they are appointed by God as the proofs of this in Quran and Sunnah are too many to recount.
In fact, the Quran argues every generic has Twelve luminaries with him, and if Christians saw John as equal to Jesus as emphasized in the Bible, that people didn't recognize him, and Elijah as equal to both, and all of them same rank as one Ahlulbayt of Aaron and Moses, they would not have gone into Jesus Worship and as for Uzair no one worshipped him from Jews but they emphasized on him more then others as God's most beloved human, but the Quran in this regard shows he was but a saint resurrected and it's only really Twelve luminaries that represent the founder such as Moses and Mohammad.
The Quran has emphasized on Ahlulbayts of the past, to make way for the present and final one - Ahlulbayt of Taha and Yaseen.
I read the Gospels and it even emphasizes on Jesus as the morning star of the family of David, which is also the family of Imran and family of Moses and family of Aaron, one chosen family of guidance.
The Torah talked about Ahlulbayt of Ibrahim not because Jews are related to them by blood which is fabricated per Quran, as Quran states, the Jews were in fact offspring of those carried in the ship of Noah. Which means not even Noah is their father, and in fact, we are not all offspring of Adam, we are all spiritual children of Adam but Adam offspring are emphasized to have had Prophethood and God's favor upon them, while Prophets coming from offspring of Adam would not need to be emphasized if all humans were offspring of Adam.
The Torah talked about Ahlulbayt of Ibrahim and emphasized on Joseph and others, to show, what a chosen household and family looks like. Then it made a covenant with respect to Aaron and his family. Yes, it goes 180 against this and accuses the first Mariam and Aaron and his family of a lot of things, but these are fabrications per Quran.
Same with Saul/Talut, Solomon/Sulaiman, they are righteous. And Lot is righteous, and makes the case why God picks one offspring out of the two founders. And he chosen Aaron to be the father of Prophets in bani-Israel.
And SARAH is the MOTHER OF ISMAIL despite what hadiths say about Hagar and accusations of slavery by hands of Ibrahim and Sarah, all lies, to make as ambiguous as possible the clear Prophecies of Mohammad and his family, and the Twelve princes means there is a king in offspring of Ismail, and Twelve will inherit him, and the king when it says Abraham is King or when Jesus emphasized he is God's anointed king and his authority is of the next world, all this means, it's spiritual authority primarily with the right to rule but their authority is not negated if people accept them or reject them.
Ibrahim - Ismail - Isaac - Yaqoub - Asbat (branches such as Yusuf) is a big theme in Quran. Lut being right hand man of Ibrahim is big theme too and he is like Aaron to Moses. He is his nephew, and Allah (swt) could've put Imams in Lut offspring or Ibrahim, but chose Ibrahim for a reason.
And he could've put in initially Ismail offspring, but out wisdom put it in Isaac, and promised a covenant of later times which is obviously what Moses means with the "the one who you will send".
God never sent any alone but always as men together, known as "the family of the reminder". Of course, the households he raised among humans and put his name in there, also had women such as the two Mariams, Sarah and Fatima (those are the ones we know) but you can make it a generalization by overwhelming majority of the Ahlulbayt being men (Imams of guidance).
All this context of chosen family and it makes understand what is meant by for example "Auli-Ibrahim" or Auli-Musa and Auli-Harun. Now, Auli-Ibrahim and their authority is used to contextualize envied humans who we then emphasized to obey in 4:59.
Get a clue before you talk about Quran. There is been a war to separate the household of the reminder from the reminder during the Prophet's (s) life till now.