Switch and PS5 and Scarlett will all be in direct competition with each other.
Switch and PS5 are in direct competition. They are both home console systems.
It doesn't matter that they are both "home console systems" that doesn't mean they are in direct competition. They will appeal to a different potential market because they are very different products with different libraries and experiences.
PlayStation and Xbox offer the same thing, Nintendo offers something different. It doesn't matter how large the install base for Switch is, and it doesn't matter what games the Switch gets.
The market that buys Fifa, CoD, GTA, Assassins Creed, Red Dead Redemption etc will buy them on PlayStation or Xbox. Even if these games were to release on the Switch their sales would be tiny by comparison.
There is a clear demand for western AAA gaming and the experiences that PlayStation/Xbox consoles offer that the Switch can never fulfil, just as there is a clear demand for Nintendo games and the experiences that the Switch offers which PlayStation/Xbox can never fulfil. As neither platform can fulfil the same demands they are not in direct competition.
A person who wants to play CoD but also wants to play Zelda doesn't suddenly lose the desire to play CoD when they buy a Switch, nor do they lose the desire to play Zelda when they purchase a PlayStation/Xbox. Some people desire both, some people only want one, the key is they're different products wanted for different reasons.
"Direct competition is a situation in which two or more businesses offer products or services that are essentially the same;" - PlayStation and Xbox, they offer a very similair experience and both cater to the same market with an emphasis on Western AAA gaming.
"Indirect competition is the conflict between vendors whose products or services are not the same but that could satisfy the same consumer need." - PlayStation/Xbox and Switch. Their products and services are very different but they could satisfy the same consumer need (entertainment/gaming).
This is the type of argument made by someone who thinks gaming started in Generation 6. 2D Mario and 2D Sonic may look different on the surface, but they are actually not that different from each other. They are both 2D platformers. A lot of former Mario fans bought a Genesis for Sonic instead. Both games basically scratch the same itch.
Switch games are not that different from Playstation games. Are you going to tell me that if a person wants to play Horizon: Zero Dawn then they would never ever consider Breath of the Wild? The games are pretty similar. Or perhaps a person likes RPGs? They might ignore Final Fantasy 16 on the PS5 and instead decide they want to play Pokemon, XC2, Octopath Traveler, and all of the other RPGs on the Switch. These games are really not that different. They scratch the same itch.
Given, there are plenty of games on both systems that are pretty different too, but if you go back before Generation 6, it was common to have home consoles with significant differences in their game libraries. The Genesis had a different feel from both the NES and the SNES, while the latter two feel similar. A lot of people still left the NES to buy a Genesis next generation.
By the same token a lot of people are going to leave the PS4 and play the Switch instead of the PS5.
This narrative is common, but the people who say it really need to do their homework. The Genesis launched in 1989 and got slaughtered by the NES that year. It also lost to the NES in 1990. The Genesis never affected NES sales in the slightest. But looking at the whole lifetime of the Genesis, it was in very close competition with the SNES. The Genesis could not affect the NES, because it had too much sales momentum behind it when the Genesis launched. But when the SNES launched, the Genesis was a cheaper system with a decent library of games already built up. Lots of people bought the Genesis instead of the SNES for those reasons.
Genesis hardware was similar to SNES, so developing games for both systems was not a big problem.
When a non-first party game is announced these days, you'll pretty much always see the PS4 logo at the end. But if the Switch logo isn't there, no one is surprised at this point, for Generation 8 games. And the process of making Generation 9 games work on the Switch is not going to get any easier.
A system's main selling point tends to be the games. And on that front, their libraries will surely only get more diverse as PS5 and Scarlett are released.
If you want to play a game like Resident Evil Remake 3, you'll probably need one of those systems.
And if you want games unique to Switch, or to play console level games on the go, you'll need a Switch.
There were some games on the SNES and Genesis that were the same, but there were also far more differences than the PS4 and XB1. At least 80% of XB1 games are also on PS4, so they really look the same. The SNES and Genesis libraries didn't have nearly so many identical games. There are quite a few instances where the SNES and Genesis have two games with the same name, but they are actually two different games. The game libraries were actually a lot more different back then. But even though their game libraries were different, Genesis still attracted fans of the NES.
You are right that a system's main selling point is the games. However Switch has lots of games and the rate they are releasing is still accelerating. Switch has no problem getting games. That means it will have no problem getting home console gamers either. The longer Sony waits to release the PS5, the more home console gamers will go to the Switch instead.