> I wonder why this olive branch of “right to exist” doesn’t also extend to the Palestinian government?

The right of a homeland for the Palestinians has been recognized since before Israel was even granted statehood by the U.N as part of the two-state solution.

https://en.wikipedia.org/wiki/Two-state_solution

The PA has been recognized since the Oslo accords in 1995.

https://en.wikipedia.org/wiki/Palestinian_National_Authority

Hamas in the Gaza strip is not recognized by Israel and its allies, but Hamas does not recognize Israel's right to exist:

https://en.wikipedia.org/wiki/Hamas_Covenant