The 6-letter word that can be extracted is:
This can be read by dividing the completed grid into 5x3 sections and highlighting the sea cells:
The solution path:
Let's start by filling in all the sea in the 0- row and column.
That leaves us with only 8 free cells in the "7" column, so all but one of them must contain ships.
We cannot have seven consecutive ship cells, so the isolated cell at the top must be ship.
That still leaves six ship cells (and one sea cell) in the lower section. The longest (linear) ship is four cells, so it must be split 4:2 or 3:3. So the single sea cell must be in the blue section, making all the green cells ship.
And wherever those ships are, all the red cells must be sea.
Now look at the rightmost column. A single ship cell in any of the green cells would create a small L-shaped or T-shaped ship that is not in the fleet. So we must have a pair of adjacent ship cells.
This tells us the 2x2 ship must use one of the green blocks, so the blue cell must be sea.
We also know that the other ship in the 7-column is the 4-ship, and the red cell must be part of it.
And, as the single 1-ship has been placed, the yellow cells must be sea. (A ship cell at the intersection of a 1-row and 1-column would be surrounded by sea giving us another 1-ship.)
Now, we still need another four ship cells in the 5-row. With the 4-ship elsewhere, this can only be 3:1 or 2:2. But purely horizontal ships here would make the entire row below sea. So we cannot have 2:2 and all the green cells must be ship.
(Apologies if the explanation here gets hard to follow, I'd be interested in suggestions for making it clearer.)
That makes all the blue cells in the 2-row below sea. There are now only three unknown cells in that row, two of which must be ship, and all of which are below known ship in the 5-row. So there are two ships oriented vertically here. The only way for that to work is if the V-ship is (partly) in the 5-row.
Finally for this section, we don't know precisely where the ship cells in that 2-row are, but they force two more (red) sea cells in the the 6-row below.
Now we can start making some real progress:
That leaves only five unknown (green) cells in the 6-row, all of which must be ship.
And that sets the location of of the O- and 4- ships on the right, filling in all the cells on that side (blue).
we also have several sea cells (red) around the 6-row. And that forces the location of the V-ship, completing the 5-row (yellow).
That gives us all the ship cells we require in both 1-columns and two of the 3-columns, making lots of cells sea (blue).
That means all remaining cells in the 3-rows must be ship (green).
And that means the incomplete 3-column must contain the last 3-ship (as it can't be 2:1) (red).
And finally the last two 2-ships are forced in the 6-column, completing the grid