Your mermaids are amphibious and can walk on land, but you haven't clarified if they can stay on land for very long. That doesn't change that they might have a vested interest in keeping a shoreline clear of land enemies, especially if the land enemies take ships out to harpoon into the sea, or if they're just using cannonballs from cliffsides as a way to harm mermaid groups at sea.
(Seeing that landlubbers aren't apparently very much on the land according to your comments, these could still be other, temporary forays by enemy mermaids - even towards waterlocked enemies, attacking in a way such that your projectiles use the sky and gravity is a good way to get the drop on them. If other mermaid groups are on the land in question).
They can fight on land themselves, but that's probably not as good either way - especially when ranged weapons come into play.
So - if they want to go to war with a shoreline nation - one way to get around that is to use siege equipment or catapults - and attacking from the sea. But siege equipment and catapults don't naturally buoy presumably, and even if they did - would have a hard time maintaining accuracy on the waves on their own. But with a boat, they could place the siege/catapult weapons on the boat, and use it as a platform to solve the stabilization problem.
They could even mount cannons on these boats and aim then, since they'll have a hard time using the saltpeter black powder gunpowder, as well as other gunpowder types that aren`t very useful underwater that they might find/mine on land..
(As an aside, you mentioned that there are both artificial and natural portals that ships can't pass through but that mermaids can; for mermaid city to mermaid city combat, I would ask the following question as some food for thought - what happens if a ship shoots a cannonball through the Blue Hole Portals? What about launched catapult loads? If they don't destroy the portal themselves, do they keep the momentum going out the side, ala the game Portal?)
Mermaid Warfare Boats might look a bit different for these needs
A lot of this "Above-water Weaponry" does sort of relying on solving the ability to stabilize siege weapons and catapults on a boat, while waves are an issue. While not a medieval tech level boat, this Martini One gives us an idea as to how mermaids might build such boats.
Though we can do older technology, the idea of negating waves and try to avoid turbulence is the main focus of that - they could add wave breakers to it, or use a medieval approach to automated wave crest correction on their floats, or simply course correct by sheer scale. After all, these boats are being manned by mermen, so the ability to sail fast might not actually be the biggest point - they could even be easily sinkable, since if they sink into the water, the mermen can easily recover them and repair/rebuild them, and none of their crew will drown.
Since they're not needing to be particularly fast in these cases if mermen can speed them up, and the size of the ship doesn't matter much either, nor redundant sinking failsafes, we can expect that they might look a bit like rafts, or Pontoon bridges - just pontoon bridges to nowhere. Or if you want to use the seabed as a level area to stabilize from regardless of the waves, sort of like Eiffel Tower style structures that can detach from the sea floor but then dig in when they're within firing range of the target - you've got the ability to go to the sea floor and ensure each possible column holding up the psuedo-tower is locked in place into the seabed when necessary.
In peacetime, some other uses
With the catapult designs, sometimes you don't want to be at war. They're still potentially useful for launching large rocks or a lot of water at a cliffside of an island or continent, breaking up the rocks on the edge of the land so that it drains into your waterways more freely broken up, either as a means to build more stone weaponry, or stole materials for other structures, or even to just make mer-made rivers and deltas so you can swim further up the the landmass to get to areas to forage where No Merman Has Gone Before.