Stravinsky should probably be the start of your argument, and someone like Cage/Reich as your midpoint and Glass as your populist revisionism endgame/full circle. Gould on Igor Stravinsky, followed by Bernstein/Gershwin/Copeland, if you want to get deeper into the new world bastardisation of the genre.
"only interaction that classical music has with the culture at large is through movies and video games"
You mean the two dominant forms of funded and marketed media in the contemporary age? What argument are you tryin to make exactly?
"jazz is publicly perceived as a novelty genre at this point"
I mean there's so much to unpack and address there it's hard to even know where to start - so I'll talk about my own direct experience in the European Domestic market. Jazz accounts for about 1% of streamed music (about the same for Classical) but accounts for closer to 5% of ticketed live music in Ireland and the UK.
There's also a huge cross-pollination in the UK Jazz/Hip-Hop scene - with particular emphasis on Grammy award winner Venna and his collaborations with the likes of Knucks etc... The South London jazz scene is also similarly dominated by the likes of drummer Yussef Dayes and keyboardist Kamaal Williams, who do a huge amount of collaborations and released the seminal 'Black Focus' album, as well as featuring on cultural touchpoints like Boiler Room etc...
London Jazz Festival pulls in 100,000 people alone annually. 2023 Guinness Cork Jazz Festival attracted over 100,000 visitors in a Metro area of 300,000.