No. I saw it. This is part of my point. The Jewish sects were concerned with how they would be considered righteous in accordance to the covenant (the Old Covenant). They focused primarily on purity laws and had a real desire that the kingdom of God would come and they be among those who are right in this kingdom. They were in effect looking for a messiah (most likely along the lines of Judas Maccabee) and they were actively pursuing this righteousness by works.Did you not see these passages written by Paul?
Rom. 9:30 What then shall we say? That the Gentiles, who did not pursue righteousness, have obtained it, righteousness that is by faith; 31 but the people of Israel, who pursued the law as the way of righteousness, have not attained their goal. 32 Why not? Because they pursued it not by faith but as if it were by works. They stumbled over the stumbling stone. 33 As it is written:
“See, I lay in Zion a stone that causes people to stumble
and a rock that makes them fall,
and the one who believes in him will never be put to shame.”
Rom. 10:1 Brothers and sisters, my heart’s desire and prayer to God for the Israelites is that they may be saved. 2 For I can testify about them that they are zealous for God, but their zeal is not based on knowledge. 3 Since they did not know the righteousness of God and sought to establish their own, they did not submit to God’s righteousness. 4 Christ is the culmination of the law so that there may be righteousness for everyone who believes.
This is different from saying that the Jews held a "works based salvation". The "saved" part is not the same.