The "next generation" after N64 was Xbox/PS2. In my previous comment, I pointed out that FPSes on consoles became viable during that time. There were FPSes on consoles even prior to Golden Eye/Perfect Dark. For instance, there were SNES ports of Doom and Wolfenstein 3D. They were just all pretty bad. Even the "good" ones like Golden Eye don't really hold up against the PC shooters of the time.
Shooters didn't become a premiere genre for consoles until the 360/PS3 era. Like I said, as far as popularity went, there was Halo and MoH (to a way lesser degree) during the Xbox/PS2 days but not much else. And then all of a sudden, shooters became the hottest genre on consoles in the mid-late 00s. That's when CoD and Battlefield made the transition over to consoles in earnest. It's when Sony invested heavily (and ultimately failed) in creating a "Halo killer". It's when CoD went from a pretty successful PC franchise to consistently being the highest selling game year after year.
As far as the PC gaming market goes. There was a dark age starting in the mid-00s. But PC gaming is very popular right now (we'll have to see what impact high GPU prices has on its future) .
For instance, Activision makes more money from the PC platform than all consoles combined.
https://www.pcgamer.com/activision-is-making-more-money-on-p...
PC has been Ubisoft's second largest platform (ahead of Xbox but behind PlayStation) since 2018
https://www.statista.com/statistics/269679/breakdown-of-ubis...
No one in the industry ignores the PC market anymore. Everyone (except Nintendo) is releasing their games on PC now even companies that weren't traditionally in the PC gaming market like Japanese publishers. Genres that had a spotty history of PC support (Sports, JRPGs, Fighting games, etc) are seeing consistent PC releases. And even Sony conceded and started releasing their exclusives on PC (years later but it's still a dramatic shift from even a few years ago).
As someone who was primarily a PC gamer in the 90s, I can tell you anecdotally that I know several people who were console gamers only 20+ years ago who are now PC gamers.