I'm a film historian, and can really only speak to manga and anime, but the animation industry as we know it has been heavily intertwined with manga since the 1960s. In the U.S., the comics industry has always been fairly separate from animation, and even film and television cartoons can be discussed separately to some degree. Not so in Japan: all three of these are so intertwined that it’s difficult to separate any one from the others

This wasn't always the case. If you go back and look at Japanese animation in the 1950s, they're very inspired by Walt Disney's films -- popular fairy tales, talking animals, musical numbers; even the drawing style looks like Disney's films. But the anime industry really ramps up in the early '60s, when Astro Boy (Tetsuwan Atomu) gets adapted. Osamu Tezuka began the Astro Boy manga in 1952, and its style was very different from what manga had been doing -- it was expressionist, it used panels somewhat like film editing; he had a very "cinematic" style, for lack of a better word. Tezuka then went to work for Toei Animation in 1958 as a writer and storyboard artist, and learned the ins and outs of the animation industry to compliment his knowledge of the manga industry. By the 1960s, he had founded his own competing anime company, Mushu Productions, and his first project was the Astro Boy TV series. This would be like Stan Lee and Steve Ditko producing a Spider-Man series -- the original author was involved with the adaptation. The best comparison in America might be The Walking Dead TV series, were Robert Kirkman authored the comic and also works as a producer on the series, and sure enough, Walking Dead is frequently cited as remaining truer to the comic than most adaptations.

Astro Boy becomes a huge hit, and it sets the model for success in the anime industry, where manga and anime are closely interrelated. Throughout the '60s, you see numerous mangas being quickly adapted into anime series. Cyborg009, for example, is a manga series in '64, then an anime film in '66 with a sequel in '67, then an anime TV series in '68, and so on. Further, a great number of writers and artists are going back and forth between manga and anime. In the US, the creative personnel at DC or Marvel were not working in animation, and the creative personnel at Hanna-Barbara or Disney Animation are not working in comics.

The '70s then sees the maturing on anime, when shows like Space Battleship Yamato and Mobile Suit Gundam move away from simplistic "good and evil" plots and fantasy technology and begin to ground their technology in more plausible and sophisticated sci-fi exposition and their morality in shades of gray, which coincides more with literary science fiction, allowing for a better overlap of audiences. Previously, anime was still largely for kids (just as it was in the US), but with these shows, we start seeing more appeal to adults as well. And, incidentally, both of these series are also re-edited as standalone feature films which do very well in theaters. By the time of the "Golden Age" of anime in 1980s, film animation, TV animation, and manga are all sharing the same otaku audience, so there's more incentive to keep these products in line with one another, and to repurpose popular franchises between the three, as they're being collected by the same audience. In America, the audience for the Spider-man comic wasn't necessarily the same audience for the Spider-man & Friends cartoon.

So perhaps the best way to think of this would be to look at Marvel Studios today. With Marvel Studios producing the Marvel Cinematic Universe, and Marvel comics and Marvel films sharing an audience, the MCU is much more intertwined with Marvel comics than superhero films have been in the past. Well, imagine if Marvel Studios was producing cartoons 30 years ago, and if writers and aritsts at Marvel were working in both animation and in comics, and you might see a much stronger relationship between the two.

Just a word of warning, this seems like this might feature heavily within the 20 years limit.

You might be better served by setting up threads on /r/SocialScience or trying /r/Anime, /r/Manga, /r/LightNovels, and /r/visualnovels for a more "brute force" method.

How did the disparate Japanese mediums/industries become so co-dependent? Do they share some common artistic origin? Are they all dominated by the same corporations? Are Japanese intellectual property laws somehow structured in a way that promotes this synergy?

You might want to try asking this on /r/anime or /r/trueanime. I can try to answer many of these questions, but I'd be violating this sub's 20 year limit.

"Visual novels" started in the early computer era when technology made it easier to do cartoon art rather than photorealistic, so they look like anime/manga for the same reasons old LucasArts or Sierra games look that way.

It is rather natural to base anime from manga because it transfers between the mediums better. Someone here noted that Tezuka Osamu is heavily influenced by Disney, but he also was a major manga artist before he tried his hand at animation.

OP's question is sort of backwards, what's more interesting than the industries being interconnected in Japan is how the American versions are disconnected. America has fragmentation between "Newspaper comic syndicates", "Comic book companies", "Young adult novel publishers", "Animation studios" and "Game publishers" as completely different companies who own their own franchises and generally do not have crossovers, except for games and movies.