Your mistake might be turning it off from both, which confuses it. Turn it off in Settings only if you want it off (although there is no good reason to, and turning them off makes Find My less useful).
Although it occurs to me what may be happening is a conflict with your instructions. Go to Settings/[your name]/Find My and tap on Find My iPhone. Do you have Find My Network turned on? If you do, that feature requires that Wi-Fi and Bluetooth be on, and possibly that overrides turning off Bluetooth and Wi-Fi. That’s just an educated guess, as I have Find My Network on, and I never turn off Bluetooth or Wi-Fi. If you want Wi-Fi and Bluetooth to stay off you will have to disable this feature.
Oh, and they also have to be on if you have Air Tags linked to the phone.