Every Path Agrees

Extreme Used by Smart Hint

List every way an island could still fill out its size — then cross off any that would break the water around it, like trapping a 2×2 pool. A cell in all the survivors is land; a cell in none of them is sea. Often the checks leave just one way, which settles the whole pocket at once.

Island (land)
Sea
Cells that establish the pattern
Where the conclusion lands

How it works

The 4 has one cell so far and five open cells to grow into — list the ways it could pick its three remaining cells. Eight different shapes fit the space.
Now check what each shape does to the water around it. A finished island is walled in sea on every side — and for seven of the eight shapes, that wall (plus the leftover cells, which would all have to become sea) traps a 2×2 pool of water or cuts the sea in two. Those shapes were never really possible.
Only one shape survives every check: the L along the bottom row. All three of its cells are land, and the pocket is settled in a single realization.
The same idea as checking a Sudoku cell's candidates against every remaining valid arrangement of a region — applied to an island's shape, with the water's own rules doing the eliminating.