The end of summer 96 had a weird feeling

Well, the PS1 and N64 took off in late 1996, which is when the 3D era really came onto its own. Teen pop on the radio was very quick to follow, as the Spice Girls started appearing a lot in early 1997.
So my point stands, that a lot changed in the 1996-1997 school year.
Even still, it wasn't exactly identical. The Spice Girls, who were predominately popular in the late 90s, are a combination of Y2K millennial teen pop, and the mid/core 90s Third British Invasion/Cool Britannia trends. By the time you get to 1999, Cool Britannia had gotten old.
As far as gaming is concerned, I will contend that late 1996-mid 1999 was largely one era dominated by the 5th generation (peaking in 1998, which is often considered one of the best years in gaming history). Late 1999 is where things start to shift with the release of the Dreamcast. Late 1999-mid 2001 is transitional between the 5th and 6th gen, with the PS2 releasing in late 2000, but not exploding until late 2001. Late 2001 is also when the Xbox and GameCube release. To me, this is the Y2K era for gaming, obviously peaking in 2000 (with titles like Space Channel 5, Jet Set Radio, and Shenmue).
I will also agree with you that the iMac played a HUGE role in establishing the Y2K era. We all know how it changed computing and Apple in general, and was influential to the aesthetics of the era. You can sort of trace that back to Steve Jobs' return to Apple, which occured at the start of 97. Really, I would say mid 1998 to late 2000 was the Y2K era of Apple, ending with the release of Mac OS X and the iBook G3 Snow in early 2001.
As far as Y2K aesthetics are concerned, you can sort of trace it all the way back to the 2nd half of 1995, with things like Windows 95 and Wipeout. Windows 95 especially helped popularize that whole dreamy sky aesthetic that became huge by the Y2K era (which I might do a thread discussing). I don't consider mid 1995 purely mid 90s anymore simply because of things like the first E3, the Sega Saturn, and Windows 95. I think mid 1994 to early 1995 is pure mid 90s, and mid 1995 to late 1996 is the transition out of that, with early 1997 really marking the point where we firmly entered the late 90s. Early 1997 to early 1998 is pure late 90s. Mid 1998 is where we shift into the Y2K era with the release of the iMac, and late 1998 shifts us even more with Pokemon, and the Game Boy Color. By early 1999 is where we firmly enter the Y2K era in my opinion. The pure Y2K era to me is early 1999 to mid 2000, with late 2000 giving rise to early 2000s things like the PS2, digitally animated SpongeBob, Nokia 3310, and Jackass. It firmly ended in late 2001 with 9/11 and 6th gen consoles taking off. Pokemania was also dead by this point, and with the decline of the anime, cable networks like Nickelodeon, Cartoon Network, and Disney Channel now dominated kid culture, firmly placing us into the 2000s in general.