Switch will spend most of its life competing against the PS5 because mid-gen upgrades won't be able to prolong the lifecycle any longer than normal. There needs to be a PS5 in 2019 because Sony knows that they can't fall too far behind PCs, that's why they launched the PS4 Pro in the first place. But who is competing against who isn't the determining factor for the widespread Wikipedia classification of generations anyway; the Dreamcast is sixth gen despite biting the dust before the GameCube and Xbox launched. For most of its life the Dreamcast was competing with the PS1 and N64.
If Sony was really worried about PCs, they wouldn't let all their consoles exclusive games launch on Steam. They even allow games they funded and published to be on PC, while they agressively get games off X1. As these titles would sell more on X1 than on PC, it would be easy to keep them off Steam and get a games advantage. The Pro model sems to compete for the higher-end market and it, maybe, intersects a bit with PCs. Anyway, its sales are already showing that this segment is way smaller than the market for the regular model.
As soon as the console still sells reasobly well, they won't release a new one. PS4 seems to be getting good price cuts, so they can reach prices lower than the PS3 did. The increased development time also makes it harder to have short gens. Rockstar will launch RDR2 in 2018. If a PS5 launch in 2019, it's quite likely that Rockstar won't ship a GTA 6 on PS4. That's quite ridiculous.
While Dreamcast bit the dust in 2001, the PS2 was responsible for its demise. It wasn't PS1 and N64 that did that. We have interviews from former Sega guys claiming that they had a target for sales before PS2 launched to deem the console viable to compete against it. They didn't make it so there wasn't possible to compete. PS2 killed it.
The Wikipedia classification is incorrect about the pre-NES era because there were Pong machines followed by two generations of video game consoles. However, at some point the American video game crash of 1983 was decided to be a cutoff point, so everything before it got lumped together, that's why the Atari 2600 and 5200 are listed as the same generation despite actually being different ones. It's just that the real third generation was so short because of the crash that somebody decided to wipe it entirely.
So where we would find the correct gen definition? Wikipedia is probably our best source.
Then there's the fact that no console manufacturer has ever labeled their systems as the generational numbers that are listed on Wikipedia, so the really important question is not what happens on Wikipedia, but what console manufacturers themselves say and do. Switch is the successor to both the Wii U and 3DS; it isn't even backwards compatible with either of these two systems, so why would Switch be the same generation as Wii U?
If we go for what they say and do, there are no more unified gens (composed by all manufacturers together). The closest we had from them was the 8 to 128 bit classification, that ended up with PS360/Wii. In this scenario, we could only count gens individually for manufactures (i.e. X1 is MS 3th gen device).
Lastly, Switch has no competition in the handheld market. If generations were defined by competition, then what would Switch be? Non-generation?
Nintendo is clearly positioning it as a home console, so we could say that the handheld market died or at least merged with home consoles. Either way, you are kind of overreaching here, aren't you? If Nintendo released handhelds alone, each gen would be defined by a new Nintendo handheld launch. If a new manufacturer entered the game, it would be classified according to the gen where it competed against Nintendo.
We also usually group handhelds with home console gens. While they don't compete directly, they compete partially for the money of consumers and have the same objective (play games).