By around what year was the pop cultural transition from the early 90s (IE the period in which it was still 'the 90s' but with a lot of 80s holdover elements) to the period pop culture remembers as 'the 90s over?

Early 1990 still had some 80s holdover elements. 1991 was when it started to feel like the 90s. And the 90s were over(to me anyway) by early 1999. 1999 atmosphere felt more like 2000.

I'd say it was some point between late 1992 and mid-1993. The early 90's, which I define as 1989-1992, wasn't just "80's holdovers" even though you had metal bands still around like Warrant, Guns N' Roses, Motley Crue, etc. I think of it also as New Jack Swing, dance/hip-house, grunge (which overlapped well into the mid 90's), and gangsta rap (also lasted well into the 90's). It was a unique period that wasn't yet the core 90's alternative rock era.

For me, it didn't really feel like a clearly different vibe from the 80s until around 1995/96.

Cars were among the last things to change.  We had a really deep and long lasting recession in Hawaii - it basically lasted the entire decade.  People kept holding on to those boxy 1980s cars nearly the entire decade.

Radio stations kept playing 80s tunes.

Fashion and hairstyles had a clear 80s influence until the middle of the decade, but it started to change early in the decade when I noticed shorts were getting longer and baggier.  I no longer saw big hair after 1995 and that "Rachel" style and "curtain" style became more common in the late 90s.  I started to see a lot of guys wearing the sagging-pants-with-underwear-exposed around 1996.

The most obvious change was, of course, in technology.  I first used a web browser in the winter of 1993.  As late was 1994, I had to explain to university-aged people what email was.  I first saw a college student with a cell phone in 1997-98.  Still, the change in technology and its impact on society and culture was nowhere near the change in the last 10-15 years or so.