Lampshading something is different than parody it’s goal is to push suspension of disbelief just a little bit further, where parody doesn’t try to maintain it.

You can’t watch “Are We the Baddies?” as a war story. It introduced such elements simply to establish who’s getting made fun of. They remain in character but that’s it, the war story plot doesn’t progress the skit just keeps hammering the parody. Some parody has a more complete story but “Scary Movie” progresses the underlying plot to make fun of different elements of the movies it’s making fun of.

Harry Potter on the other hand calls out many of the tropes it’s using. House of the lions vs house of the snakes, guess who’s supposed to be the hero and who the villain. Except the characters once introduced are telling an actual story.

Snow Crash is between those extremes but focuses too much on the underlying story and its characters to be an actual parody. Over the top elements exist in the world, but they are played straight more Gulliver's Travels than Spaceballs.

Parody or not, I wish I could apply for citizenship at Mr. Lee's Greater Hong Kong

I forget the term for it but there is a thing in anime subgenres where something comes out that is a kid of rejection/critique of the previous genre and acts as a kind of pseudo parody that afterwards sets a new direction and redefines the genre. Often these are hard to understand unless one is already familiar with the trends and tropes that it is critiquing. A good example is neon genesis evangelion, it's a critism of the mecha subgenre that came before it, but changed the way the mecha subgenre was afterwards. I'm told hunter x hunter is the same kind of redefining pseudo parody with the battle shonen genre, but I'm less familiar with that.

I feel like snow crash it's kinda along those lines.

Are you thinking of "deconstruction"?

I think NGE as a critique or deconstruction of mecha anime is often overstated. For instance Shinji as a subversion of the typical macho teenage boy mecha protagonist... well there was already quite a lot of mecha anime with non-traditional protagonists, such as Patlabor's Noa Izumi who is neither a boy nor a teenager. Patlabor broke the mold in numerous other ways besides, more-so and better than NGE. Mecha (e.g. Labors) foremost as industrial tools instead of super-science weapons with mysterious powers. Pilots being professional young adults who mostly act like it. Most of life for the crew being mundane routine responding to DUIs instead of grand save-the-world plots (a few military coups notwithstanding.) I think in these regards, NGE stays closer to the traditional mecha formula that it ostensibly deconstructs.

I think where NGE really shines is the art, design, animation, which are all stunning. I have much respect for NGE, but specifically as a deconstruction of the mecha genre I've never been impressed.

And Martian Successor Nadesico is an excellent parody of the giant robot/mecha genre. If you liked Patlabor, you might enjoy that.