I do think that there is a sharp dividing line as "Old School" and "New School" was first defined or coined: i.e., TSR D&Ds vs. WotC D&Ds. "New School D&D" was indeed initially defined as 3e D&D and onwards. That is generally how I see "Old School" vs. "New School," in a more technical sense of publishing eras. And dare I say it, "New School" vs. "Old School" was something of a tacit agreement with the idea of "system matters," as some gamers who wanted to keep playing TSR era games weren't connecting with 3e as a game system. But as you say, in some senses, the strands of "New School" play culture were already present in the big tent play culture of TSR D&D.
However...
.... one of the problems in this thread involves unclear terms being used. Some people are conflating Old School D&D with OSR, especially the later strands of it, namely philosophical OSR. (Not claiming that
@Reynard is doing this, but his posts highlight topic points where vagueness can lead to confusion.)
Old School D&D - TSR-era D&Ds: Oe-2e D&D, B/X, BECMI, etc.
New School D&D - WotC-era D&Ds: 3e-5e D&D+, but also PF1-2, etc.
Old School Revolution/Renaissance:*
- Wave 1 - Retro Clones: originally a way to republish and continue playing TSR D&Ds under the OGL
- Wave 2 - Philsophical OSR: a (somewhat revisionist) strand of OSR influenced by the Forge and interested in the sort of philosophical underpinnings of old school games, TSR D&D compatible but increasingly TSR D&D-adjacent
- Wave 3 - NuSR/NSR:** TSR incompatible games, but adhere to OSR principles
The Hickman Revolution, for example, arguably became something of a convenient scapegoat or rallying cry for Wave 2 and Wave 3 OSR. The Hickman Revolution didn't really matter for Wave 1, who were mostly interested in playing older editions, but it was a sore point for those who developed the OSR Principles. Again, there was undoubtedly influence in Wave 2-3 OSR from the Forge, namely in this case a certain hostility to GM authored story, linearity, and force. (The Forge was complaining about similar things around the same time in regards to Vampire the Masquerade.)
* There are more waves and strands than this,
as read here, but this is more of a convenience.
** Confusingly, there were also attempts to use "New School Renaissance" (NSR) as the name for a movement when there was a surge of renewed interest in 4e D&D
To speak more directly to this point, when you keep in mind what I discuss above, there are really two sense of when "New School" starts:
(1) WotC era D&D, as per "TSR Retroclone-inclined OSR" - the games are now not as compatible as TSR D&Ds were with each other
(2) Hickman Revolution and the emerging dominance of "Trad play culture," as per "Philosophical OSR."
We could even have two timeline to show periods when these senses of Old/New School overlap and contrast.