Yes you are required to file the CA 568 if you are a California LLC not taxed as a corporation.
From the FTB:
There is a first-year exemption from the $800.00 annual tax to limited partnerships, limited liability partnerships, and limited liability companies that organize or register with the California Secretary of State on or after January 1, 2021, and before January 1, 2024.
LLCs classified as disregarded entities or as partnerships are subject to an $800 annual tax. This applies if they do business in California or if the SOS accepts their Articles of Organization (LLC-1) or Application for Registration as a Foreign Limited Liability Company (LLC-5). LLCs organized or registered in California are subject to the annual tax even if they conduct no business in California (R&TC Section 17941(b)(1)). For taxable years beginning on or after January 1, 2011, an LLC organized in California is doing business in California (R&TC Section 23101(b)(1)).