Rules: (Nurikabe section shamelessly stolen from an earlier puzzle by @jafe)
- Numbered cells are unshaded.
- Unshaded cells are divided into regions, all of which contain exactly one number. The number indicates how many unshaded cells there are in that region.
- SPECIAL RULE: the regions will form a tetromino set, with rotation and reflection allowed.
- Regions of unshaded cells cannot be (orthogonally) adjacent to one another, but they may touch at a corner.
- All shaded cells must be connected.
- There are no groups of shaded cells that form a 2 × 2 square anywhere in the grid.
I've included all available tetrominoes as a reference.
A playable version of this puzzle can be found here. The link leads to a puzz.link editor. Note that this editor won't force you to use the tetromino rule, and it has a timer.
The first answer with a fully-explained logical solution path will get the checkmark. I welcome multiple answers, if later ones can show a better-explained, more elegant, or significantly different path.
Tabular transcription good for copying into a spreadsheet (ignore the header row; the first row with a number is the first row of the puzzle):