*** Moved from K1 Process & Procedures to the Philippine regional forum, for country-specific input ***
As long as you have your final divorce decree (and have met your beneficiary in person at least once within the past 2 years), you may already file the I-129F petition to start the K1 process. That said, consider pursuing the CR1 spouse visa instead for your new Filipina, since you seem to be ready to get married soon anyway. Even if you cannot get married again in the Philippines, you can get married abroad or through Utah zoom wedding.
Are you a dual PH-US citizen? If you are not Filipino, then there is no need at all for you to file for annulment in the Philippines. If marrying in the Philippines and having a marriage certificate issued by PSA is super important for you, then you could file for Recognition of Foreign Divorce instead, assuming you are not Filipino. Simpler and faster than an annulment. If a PSA marriage certificate is not important to you, no need to even bother with Recognition of Foreign Divorce.
Note that marrying with a PH marriage license means that your beneficiary will not be pursuing the K1 visa path, as K1 requires marriage in the US. If you do pursue K1 and get married in the US, you and your new wife cannot legally get married again in the PH. You are free to hold a ceremony in the PH for renewal of vows (not wedding), but there should be no PH marriage license.
USC petitioner's CENOMAR/CEMAR would not matter as long as you have your final divorce decree from NY.