OP here (hi!). I have awarded the green checkmark to @MOehm's answer for being the most complete (the LITS solved state is presented, the hidden connecting wall is identified, and the final one-word answer has been found). I also highly commend the answer by @Sconibulus for verbalising a logical path through the LITS grid deduction process and being first to identify many of the connecting wall connections.
However, what this question still lacks is a step-by-step explanation of the LITS solution process with diagrams to make it easier to follow. I now present this here for future reference (along with a explanations of a few Easter Eggs that have not so far been uncovered...).
Two shapes must be wholly shaded from the start. We then notice that the tetromino in the large 'background' shape MUST be placed in a position where it links the stranded S-piece to the rest of the letter mass. We can thus rule out the majority of these background cells, noting at the same time that the T-piece in the top-right corner must be linked through the rightmost C-area, and only an S-piece will permit this.
There are also a number of other cells that MUST be shaded due to the constraints of their areas, regardless of what shape they end up being.
Focus on the L-area in the bottom-right...
It is impossible for the tetromino in this area to extend any further upwards. If it did, regardless of the shape forced in the neighbouring rectangle-area, it becomes impossible to place a tetromino in the other adjacent L-area:
As a result, this L-area must contain an L-shape and not border the tetromino in the other L-area (which would be forced to be a second illegally-touching L).
A key deduction. Look at the adjacent O and N-areas in the top-left quadrant...
Do the tetrominoes in these 2 shapes need to abut each other - or is there a way for the O-area to be linked to the W-area at the same time as the stranded S-piece?
A little thought (noting that the O-area MUST contain an L-tetromino) shows that this hypothetical O-S-W linkage is impossible without forming a 2x2 shaded area or two identical tetrominoes touching. (For an exhaustive exploration of all possibilities, see the image below...)
As a result, the tetrominos in the O and N areas must abut...
Furthermore, the N-area cannot contain a second L-piece, and so must contain an I-piece. This forces the placement of two adjacent tetrominoes.
Also, while we're thinking about the N-areas in general, note that if the E-area connected to its adjacent N-area with an L-piece, this would force a second illegally-touching L-piece in the N-area; we can deduce the states of a couple more cells in the E-area as a result...
Focussing now on the rectangle in the top-left quadrant...
The tetromino in this area must connect with the L-piece in the adjacent O-area. As a result, the centre-right cell within this shape MUST be shaded (since if, alternatively, the bottom-right cell were shaded this would force two illegally-touching L-pieces). This forces some cells in the adjacent C-area:
This now leaves only one option for connecting the stranded S-piece to the rest of the tetromino mass - via an L-shape in the background-area, and an S-shape in the W-area:
Focus next on the A-area...
The cell above the black space MUST be shaded, for connectivity. A few other spaces in the shape can be ruled out due to being unreachable or forcing two touching identical tetrominoes.
Importantly, we still need to place 3 I-pieces and there are now only 3 shapes remaining which could contain one! The I-pieces in the remaining C- and L-areas are fixed; the remaining I-piece must occupy one side of the remaining N-area.
This final I-piece can then be placed by noting that the E-area must connect to the N-area:
And finally, there is only one way to place the tetromino in the A-area (using an L-shape) and the last unresolved rectangle must contain an S-piece since we have used our full complement of T-shapes:
I had a lot of fun choosing 'spare' words to include in the grid. Most were chosen pretty much at random, using words that commonly have multiple connections; however, some were specifically chosen to conceal messages or just for fun...
Just for fun:
1. As spotted by @DarrelHoffman in comments, I chose to fill the 5 background-area squares that are impossible to connect to any other area with ridiculously long words.
2. There's also a concealed reference to the 2004 Will Ferrell movie, Anchorman lurking in the top row of the grid.
3. In several instances I laid red herring words that looked like they might be related to each other, in vague attempts to trap solvers trying to shortcut the logic of the LITS. Notably, the rectangle between the two L-areas contains three character names from Doctor Who (one of which was required for the connecting wall, the others not so much). Elsewhere you might spot partial names of Marvel's Avengers, Oscar-winning movies and more...
A concealed instruction:
Just in case anyone was in any doubt that the second stage of the puzzle required the construction of 4 separate connecting walls grouped by common tetromino shapes, I laid a hidden instruction within the puzzle...
If anybody happened to notice that there were a lot of animal names in the grid and then listed them, they would notice that their initials read in order spelled out 'ONE WALL PER LITS SHAPE'.
Alternatively, if anybody noticed that the words beneath the centre of the T-area spelled out 'SECRET MESSAGE: READ ANIMAL START LETTERS. OVER.' this would direct them towards this!
My thanks to all who attempted this puzzle :)