Don't the branches here stand for the nation
of the jews in Jesus's day?

Not at all.

The branches stand for people, Jews yes, but not the jewish nation.

In that passage (Ro.11)
- The Hebrew "nation" is simply called "Israel".

- The "Olive tree" is God's kingdom which, before Christ, had been tied to the nation of Israel.

- The "Root" is the spiritual heritage of God's people, (the patriarchs, the written scriptures, the prophets etc)

- The ingrafted "wild olive tree" is the gentile church.

- The "branches" are individual people.

- The "fallen branches" are Jews who refused to believe in Jesus and therefore fell from being attatched to the tree.

The situation was this, some Gentile Christians were feeling superior to Jewish Christians and treating them as inferior within the church, thinking that because God had cast off Israel from being "his people" and replaced it with the church, that Jews were somehow inferior in God's eyes to Gentiles.

The whole passage is telling the Gentile Christians that they are not superior to Jewish Christians. Jews can be grafted back into the tree just as easily as can Gentiles and Gentiles can fall just as easily as can Jews.

"Boast not against the branches" Same thing here Branches means Nation of the jews too

No it doesn't, it means individual Jews, people, not a nation.