It is OpenTTD history that deserves to be remembered. <h/t to The History Guy
The first formal suggestion for creating it was made by Sgt_Poulet in early 2004. His description of what a seaplane airport would look like would effectively be the design that most others would follow in the decade to come - a modified TTD small airport with docks/quays and landing strip in water.
A few months later, Born Acorn offered his own idea of using the seaplane port as a means to transport oil to and from the sea-based oil rigs. Later he gives a small history of the Boeing 314, a popular choice for a seaplane and an example of how they could be useful in the game. ThorRune would offer up one of the first mock-ups of such a seaport, and Dominik81 and Mr. X would also provide their own (presented in-order). This discussion would continue on in spurts for another two years, and would be referenced in other posts discussing the proposal.
Near the end of 2006, Lt_Gable would draw the Latecoere 631, giving us our first seaplane sprites. He also would draw his own vision of a seaplane port, which generated some more discussion of how to code such a thing.
In 2006-2007, there was discussion about writing some new code for adding NewGRF airports. Richk67's proposal included designs for a potential seaplane port. By April 2009, he posted the first images of a working seaplane port within his proposed expansions of the NewGRF spec. Unfortunately, his proposals were rejected and the project was terminated.
RichK and a few others would also draw some early seaplane airports in the middle of 2007 which eventually evolved into the design he posted in 2009. In late 2007 another discussion on seaplane airports was started, to which RichK contributed more information about expanding the proposed NewsGRF specs. In early 2008 he published information on coding airplanes which allowed Grigory1 to code some of his planes to be compatible. I should also mention that at some point before this, PikkaBird had also coded support for the seaplanes into AV8 (sometime before v1.331, but I haven't found exactly when yet).
In May 2008, Grigory1 would publish the Beriev Be-200, compatible with RichK's specs. A few days later 5234jah would publish the Boeing 314. In August 2008 Zepherys looked into developing a seaplane NewGRF but eventually abandoned it.
In October 2011 PikkaBird officially publishes AV8 2.0, with the Short S.26 Empire flying boat, available as both a land and seaplane. In March 2012 version 2.1 added the Short S.7 Calcutta and some sound effects.
A few days after AV8 2.0 was published, Quast65 published the first NewGRF seaplane airport that works within current OpenTTD specs. And, I just now noticed that Quast's concrete docks were actually drawn by me! How did I miss that? LOL. Unfortunately it's not a straight drop-in replacement, as it requires some advanced techniques to properly build it. It's a kludge, but a kludge that works.
In April 2015, Quast's work would eventually lead to Supercheese adding a small seaplane airport to OpenGFX+ Airports, offering full 360-degree rotation. Coincidentally enough, I offered to draw the dock sprites for this set. Hoorah!

A week later, Roslav would expand upon that work with a patch version of the airport, but unfortunately was left abandoned but functional. No patch pack has adopted it, however.
That brings us up to date, We have a working-but-not-perfect seaplane airport and we have some planes we can land them on. We also, by the way, also have the Zeppelins in AV8 and the much older Planeset, which were initially launched from water-based sheds historically. Hopefully this summary will be useful to anybody who is researching implementing seaplanes or seaplane airports in a future project.