There are lots of situations where underwater races will want to send messages to each other, write in spell books, create maps, etc.
Are there any examples out there in D&D lore (any edition, any canonical setting, Forgotten Realms preferred) of aquatic writing?
The sahuagin, merfolk, and sea elves of Eberron all have sophisticated cultures. The descriptions often imply the existence of writing, but it is not often explicitly stated nor desribed.
Sahuagin and sea elves in Eberron use engravings. Descriptions in Ghosts of Saltmarsh describe some in Sahuagin structures:
page 127:
Glowing symbols and strange designs are engraved into the walls of this place
page 130:
One side of the medallion carries an engraving of a shark. The other side's engraving depicts a dozen tridents offset in a circle to form the shape of a star. This symbol is the baron's personal seal
Exploring Eberron (p.198) has references to engravings used by sea elves:
... connected by rune-lines—glowing patterns engraved in the sea-bed
In Exploring Eberron, there is description of the inhabitants of the Thunder Sea. A tangential reference to the existence of written records is the undersea city Hal'daan which includes in it's description:
This city also holds the bureaucratic archives of the Dominion.
Likely candidates, but not explicitly referenced as such, for creating written or symbolic representations of messages are fabricate and korlass. As detailed in Exploring Eberron on page 194:
[sahuagin] magewrights can cast fabricate as a ritual, shaping raw materials into their desired form through magic.
[sahuagin] also uses a substance called korlass (dreamstone), formed from dreamer biomass, as an industrial material; it can be sculpted like clay, then fixed in its shape by a magewright ritual.
Sure, looking for any examples of how writing can be done underwater really, as there are so few that I can find
Not exactly an example from D&D or Pathfinder, but since the OP explained on a comment how they need any example of how to make underwater texts, I'll instead explain how I personally do things on my works where underwater writing is concerned.
Dealing with liquids while living inside another liquid is messy. Water, by the sheer nature of it, makes some fine movements a bit more complicated. It is harder to make things move underwater, it is harder to make them stop. It is harder to be precise, and writing with ink is a precise thing. A very precise thing.
That said, writing is all about storing information for later. As long as we can get information stored, it's all good. You don't need ink.
Anything that can be used to make symbols is enough. And that anything can be holes.
That's punched tape. It was used way back then to store information in a way computers could read later on. While not exactly as elegant of a writing format as Russian Cursive, it can get the job done when you can't reliably use ink. You just need some treated algae, water-resistant leather, or any other "sheet-like" material that you poke holes on, and you're set.
I personally use this method when writing stories or games that deal with one of my underwater races. It is easy to explain, it is easy to draw, and it is easy to make props out. It is alien enough to look like a different language, while being easy to translate if you have a dictionary at hand. More importantly, it is easy to demonstrate how a given race would use this method on their day-to-day lives: describing a scribe taking notes is not any harder than explaining a person using a pen-like device to poke holes in a sheet of shark leather bound to a wooden frame.
You can even do this live for your players, taking some paper and "poking down" some text in merfolkian live for then using a sharpened pencil.
More importantly, however, is that this method looks and feels very different from both regular western writing and eastern writing, while still being believable and practical. It enables one to create a very different, unique aesthetic, based entirely on patterns of dots, to races that are usually a little more than "elves with fins".
The answer to this in Forgotten Realms lies in the Threat from the Sea series:
In Rising Tide:
"The sahuagin books were created of string bits of stone and shell on knotted thongs, each tied to a ring of bone or sinew. The way the shells, knots, and stones hung together represented sounds in the sahuagin tongue. Just shaking the sahuagin book created a series of sounds that gave the title. That was why many referred to them as singing bundles." (p.10)
Under Fallen Stars has this about sea elf books:
"Shelves and bookcases covered every wall, designed to hold every tome whether it was inscribed on cut stone or on delicate gold foil." (p.37)
"Most of the books were written in special pastes that hardened and adhered permanently to pages that were cut from the shells of giant clams. A lot of time went into the creation of each book, so they were highly prized. Some of them were even tonal books, pieced together with crystals like the saceddar and designed to be struck by a tiny mallet in order to be read. Still others were merely books ensorcelled to withstand the sea." (p.265)
The module U3: The Final Enemy shows us two levels of an underwater sahuagin lair, and is perhaps the most detailed description of an underwater setting in first edition. A mix of actual writing and elements that could be used for writing are described. Some were made entirely underwater, some were apparently partially made above water and then finished once they were brought underwater, and some were made above water but designed to function underwater.
Magic
A cleric's room contains a trap with a glyph of warding, as does the entrance to a treasure room. In first edition a such a glyph was "a powerful inscription magically drawn".
Carving / Engraving
One of the treasures in the chieftain's room is a
coral statuette of a shark
If the sahuagin carve in coral to make statues, they could do so to make writing. Several places in the module mention 'dressed' (shaped) stone. A coffer in a barracks room contains a "carved coral rod" and a cleric's quarters contain an engraved table-top. The quarters of the high priestess contain an engraved table-top as well as 'ornately carved benches'. The baron's black coral throne is ornately carved and his silver medallion is engraved on both sides. There is a stone chess board with carved stone pieces and carved coral pieces.
Beadwork
A chieftain in the module has a
gold armband set with coral beads
The gold was likely forged above water but the beads may have been set underwater. With different colors of coral and beads set in different positions, alphabetic or pictographic words could be written. Other treasures in the module include
a silver bracelet set with turquoise beads...an electrum pendant set with coral beads...a silver bangle set with coral beads...a gold collar set with amber beads (x2)...a gold collar set with coral beads...a gold armband set with coral beads (x3)...a gold armband set with amber beads...
Tiles
Most of the rooms in the lair are tiled, generally with one color for the walls and another for the ceiling, and sometimes a third for the floor. Within the module, this is just used for atmospheric effects rather than writing purposes. However, one can easily imagine tiles of two different colors being arranged to write words, make maps, etc. The limitations would be the smallest size of tiles possible and the size of the surface to be tiled. Within the module, the tiling work was done in the rooms while they were above water, and once the room was complete it was flooded. The stated reason for this was because the tiling work itself was performed by air-breathing slaves, but it is also implied that these are normal ceramic tiles that would need to be fired above water and placed with a mortar that dries in air. An aquatic race could do this on-site underwater more as a mosaic with colored snail shells and a harvested adhesive like that from barnacles.
Writing for underwater
While not writing performed by an underwater race, the players may encounter a magic-user whose adventuring party has been commissioned to scout a sahuagin lair. His three spellbooks were prepared with paper-on-ink as typical for land-dwellers, but later each page was coated with a clear varnish so that they would be visible and usable underwater.
Three small books which are Elmo’s travelling spell books. These have been painted over, cover and pages, with a hard transparent varnish to protect them from the effects of immersion in salt water
