I have a few things to note that have not yet been covered in other answers.
* Flexibility: traditionally, wooden shipbuilding used a time-consuming process called Steam Bending to temporarily soften pieces of wood in order to plastically deform them into the necessary curved shapes. If a mage can do that faster with magic, construction could go substantially faster.
* Structure: A ship's frame bears most of the forces the ship is subjected to. In theory a hull could be made thick enough to withstand such forces, but to do so in our reality would require so much extra wood and add so much extra weight that it's never done. Instead, hulls are made as thin as is practical given the conditions they will face (coastal and river [brown-water and green-water] ships can have thinner hulls than high-seas [blue-water] ships, trading ships can have thinner hulls than warships, et cetera). The hull is mounted on a complex structural frame that attempts to maximize strength while minimizing weight. The complexity is partially caused by the fact that wood's strength against any force varies greatly by the force's orientation relative to the grain, and thus the frame is made of many short timbers arranged to be in the best direction for the stresses each will endure, and braced at the joints with more timbers that distribute the stresses across the entire frame rather than letting it concentrate at a single point. In your world, however, the ability to seamlessly fuse pieces of wood to the extent of joining their grain structure allows you to do away with a good portion of this structure and make your ships lighter and more spacious for the same strength. The densification helps with reclaiming a bit of interior space as well. You still need extensive bracing fore and aft and beam to beam to resist buckling, bending, and twisting, but not nearly as much. Care does still need to be taken with the directions of the fused wood grains, as mentioned. The hull would benefit by having layered grain structures orthogonal to each other for maximum pressure resistance - you could produce something like a Monocoque made of a fusion of Marine Plywood and Cross-Laminated Timber, which would let you have even stronger hulls for the same weight.
* Failure modes: the Strength of Materials involves more than hardness. 308
You said that the magic system can improve wood's Impact Strength, but you also want to figure out what your magic can and cannot do in terms of Compressive Strength, Tensile Strength, and Fatigue Strength. Under normal conditions, wood cracks when any of these strengths are exceeded - and the more force it took to reach the breaking point, the more dramatic it will be when that force is released.
* Fire resistance: Densified wood tends to char rather than be consumed by fire, which will help limit the spread of shipboard fires. Ropes and sails will still be extremely vulnerable, unless your world includes some way of fireproofing them as well.
* Masts and Rigging: Mast failure by bending and ultimately cracking (known as a "sprung mast" if it doesn't just snap off completely) became a major problem as ships got bigger and got more sails, which put extreme strain on the masts. In our world, this was combated by adding extensive webs of "standing rigging", strong ropes that ran between the top of a mast and the frame of the upper deck in the same way that a modern radio tower is supported by guy wires. As masts got ever taller and the forces on masts became ever greater, even extensive standing rigging was often insufficient, and it became common and then standard for masts to be reinforced by wrapping them at intervals with tightly-coiled rope and/or iron hoops. These helped keep the wood fibers from separating under bending stress. With your magic, it sounds like it would be feasible to clad a vertically-oriented core with a layer of horizontally-oriented fibers joined into complete loops, which should offer comparable strength increases. There is also the potential of magically joining wooden beams horizontally between masts to add support in compression (compared to rope, which is only strong in tension) and diagonally from frame to mast to act as buttresses.
* Biofouling: All ships and boats (and any other structures in the water), no matter what they're made of, are subject to the buildup of a layer of aquatic life including seaweed, algae, barnacles, tube worms, and hundreds of other species. This rapid buildup makes the surface increasingly rough, causing turbulence and drag that can slow a ship by up to 10%. Ships need to regularly undergo maintenance to clean their hulls and counter these effects. Wooden ships also have to deal with Shipworms, a group of molluscs that bore into - and eventually destroy - any submerged wood. 308