In terms of the broad swathe of writing about hip-hop, a lot of it is more focused on the period that runs from the 1970s, when hip-hop began, through to the mid-1990s, when we started to see the current infrastructure of mainstream hip-hop emerge, and with the deaths of the Notorious B.I.G. and 2Pac as a sort of natural stopping point. So the book Original Gangstas: The Untold Story of Dr. Dre, Eazy-E, Ice Cube, Tupac Shakur, and the Birth of West Coast Rap by Ben Westhoff doesn't go as far as discussing Dr Dre's 2001 album, for example. This, I think, means that the final word on 'Forgot About Dre' is probably yet to be said.

That said, some of the context behind 'Forgot About Dre' is likely discussed in Westhoff's book is that in the wake of the death of 2Pac (who Dr. Dre collaborated with on 'California Love', probably 2Pac's biggest worldwide hit), Dr. Dre had left Suge Knight's Death Row Records in early 1996 in order to start Aftermath Entertainment with music industry insider Jimmy Iovine, its first release being a November 1996 compilation album, Dr. Dre Presents The Aftermath, featuring several examples of Dr. Dre's production. However, it's fair to say that Aftermath as a company did not have a particularly successful 1997 and 1998 by Dr. Dre's previous chart-topping standards; his main project of 1997 seems to have been producing the hip-hop supergroup The Firm (which most prominently featured Nas), whose album hit #1 on the Billboard charts, but which didn't have any strongly charting singles. 1998's main output for Dr. Dre was 'Zoom', a single from the Bulworth soundtrack with LL Cool J, which also failed to set the singles charts alight.

By the time that Dr. Dre's 2001 album was released in November 1999, however, Dr. Dre was very prominently the producer of, and associated with Eminem, the biggest new star of 1999 and someone signed to Aftermath. Dr. Dre is namechecked in and then immediately has a cameo in Eminem's 'My Name Is' (released in January 1999), and appears as the voice of reason on Eminem's 'Guilty Conscience' (released in July 1999).

This is the implicit context of 'Forgot About Dre'; the song features Eminem not only as a featured rapper, but also the ghostwriter of the track - the rapid-fire, off-kilter flow of 'Forgot About Dre' is blatantly a dead giveaway that Eminem wrote those lyrics. In a 2019 piece on Ambrosia For Heads, Dre is quoted as saying as much:

[Eminem] wrote “Forgot About Dre,” which would become a video single. “He wrote the song for me and Snoop, originally,” remembers Dre. “He laid the reference vocals for Snoop, and I liked the way it sounded [better].” That’s the version that made the LP. Dre never addresses his haters by name, but the song gave [Dre] the latest word. He addressed the lukewarm response to 1996’s compilation as well as the jeers from the cheap seats of the music industry.

In a similar vein, Dr. Dre, as interviewed by Vibe in 2019, says that Eminem came to him with the lyrics:

The Hollywood Walk of Fame star recipient said Em originally wrote the song with the former and Snoop Dogg in mind, laying down reference vocals for Uncle Snoop which sounded appealing to Dre.

"I had no idea what triggered him to write that song," he shared. "He just came in with those lyrics and we wrote some music to it and that was that."

Of course, while Eminem wrote the song, Dre as producer and record company co-owner had ultimate control of it, and so at least implicitly approved its message (though given the populist nature of the music, I'd caution taking the message of that song as something Dr. Dre believes himself as opposed to a message he thought would sell records). The song starts out with an implicit recognition of Dr. Dre's lack of success at Aftermath:

Y'all know me, still the same OG

But I been low-key

Dre's lyric, written by Eminem, then discusses all the trappings of success (implying that Dre, unlike his haters, can afford boats and snowmobiles and skis), and reminds listeners of his track record with Snoop Dogg, The Chronic and NWA:

Who you think taught you to smoke trees?

Who you think brought you the oldies?

Eazy-E's, Ice Cube's, and D.O.C.'s

The Snoop D-O-double-G's

Finally, Dre moves on to address the specifics of Aftermath's track record:

Y'all better listen up closely

All you n****s that said that I turned pop

Or The Firm flopped

Y'all are the reason that Dre ain't been gettin' no sleep

So fuck y'all, all of y'all!

Here, he appears to be implying that he is motivated to prove his critics wrong, and that 'Forgot About Dre' and its inevitable success is, effectively the proof in the pudding. Dr. Dre says as much in a contemporary Rolling Stone interview:

[Rolling Stone:] A few songs are about re-establishing your reputation. Do you really think people forgot?

There’s only a couple of songs where I’m defensive. I’m just responding to the shit I was hearing. People were saying that I didn’t have it anymore and that I hadn’t made a good record in years. I just can’t ignore that shit. I had to respond. So this is my “Shut the fuck up” album. Now what do you people have to say?