This puzzle’s theme is impressed by one from Grandmaster Puzzles’ “The Art of Puzzles”, however the puzzle itself is unique.

Rules: (Nurikabe part shamelessly stolen from an earlier puzzle by @jafe)

• Numbered cells are unshaded.
• Unshaded cells are divided into areas, all of which comprise precisely one quantity. The quantity signifies what number of unshaded cells there are in that area.
• SPECIAL RULE: the areas will kind a tetromino set, with rotation and reflection allowed.
• Regions of unshaded cells can’t be (orthogonally) adjoining to at least one one other, however they could contact at a nook.
• All shaded cells should be related.
• There are not any teams of shaded cells that kind a 2 × 2 sq. anyplace within the grid.

I’ve included all out there tetrominoes as a reference. In addition to the image, here’s a Penpa hyperlink (no automated reply checking) and a CSV:

,,,,,,,
,,,4,,,4,
,,,,,,,
,,,,,,,
,,4,,,,4,
,,,4,,,,

Answers are anticipated to incorporate an outline of their resolve path. This isn’t a really massive puzzle, and you may in all probability clarify the logical steps in a solely few progress photos, however please chorus from posting a solution with solely the ultimate answer.

Special due to @Stiv for playtesting the puzzle!