Do seaplanes need to say their intentions before landing on uncontrolled water? I know you don't need to say your intentions to take off in uncotrolled water but what about landing on one?
Only if the water is within a Mandatory Frequency zone established around an uncontrolled airport with adjacent water landing areas. An MF is a CATF that must be used to broadcast intentions IF you have a radio.
MFs are common in Commonwealth countries but rare in the US (Ketchikan AL apparently has mandatory use of its CATF). With a MF, if you have a radio, you are required to use it. If NORDO, well, you don't and NORDO airplanes are free to come and go from uncontrolled airports.
Otherwise, as with an uncontrolled land airport, you are not legally required to broadcast your intentions in any situation with a water aerodrome in uncontrolled airspace, and don't even need a radio. You just use common sense and do what others are doing at a particular landing area if there is other traffic and a common radio frequency being used.
Coming and going from remote lakes when I was bush flying, in the middle of nowhere, I never broadcast intentions when there was nobody else around, only if a lake had other airplanes coming and going.