Is working at the investment company affiliated with the Pension Authority, which manages funds mostly in un-Islamic investments, deposits, and shares in usurious banks and companies, permissible in Islamic law?

Working in an organization that is not involved in forbidden transactions is permissible. As for forbidden contracts, whether with usurious banks or others, they are forbidden, based on the Almighty's saying: "And do not cooperate in sin and aggression." The Prophet, peace and blessings be upon him, cursed the one who consumes usury, the one who feeds it, its scribe, and its two witnesses.