score:3
No, passports in Israel are issued by the Ministry of Interior. The timeline may be affected by the Ministry of the Interior being swamped with passport requests and lack of appointment slots, though. I doubt you can turn this around in 3 weeks (if you intend to visit Israel for the purpose of passport renewal).
You may be able to get an emergency 1-yr passport at the airport on the spot, costs double the price.
Until the end of this year, Israelis who have foreign passports are allowed to use their foreign passports to enter and leave the country (see the announcement at the Israeli consulate in SF web page I linked to in the other answer).