Yes, you will need to upgrade manually. How far you will get depends on whether you are on the “stable” or the “dev(eloper)” release of /e/OS for the FP3. Your current full version number should clearly indicate this at the end. “stable” for the FP3 is still on S (Android 12), “dev” is on T (Android 13).
P.S.: As you are on 1.5 and said you’re on Android 10, you can only be on dev right now.