Third Party Support has never been a selling point for Nintendo. At least nowhere near as much as it is for Sony and Microsoft. When the casual audience look for games/reasons to buy a PlayStation or Xbox, they look primarily for Call of Duty, FIFA, Grand Theft Auto, and NBA 2K, games that have become synonymous with the PlayStation and Xbox brands, more than even most of Sony and Microsoft's own first party franchises. But when they look for games/reasons to buy a Nintendo system, they look for Mario, Pokemon, Smash Bros., and Zelda. Nintendo games. It's not going to hurt the Switch in any significant way, if at all, because nobody, at this or any point, expected the Switch to have that level of 3rd party support.
Think of it this way. Imagine a scenario where all of the 3rd party developers, major and indie, Western and Japanese, from EA and Activision to Square Enix and Capcom. All of them... just vanished of the face of the earth. If Thanos snapped his fingers and made all the 3rd party developers disappear and it's just Sony, Microsoft, Nintendo, and all their subsidiaries and studios as the only game developers on the planet... Sony and Microsoft... are in a lot of trouble. They are in DEEP shit. They're in the middle of the ocean without a life vest and it's sink or swim. Microsoft much more than Sony. Sony could make it. It's not going to easy by any means, but they could make it. Meanwhile, Microsoft would pretty much be fucked... And they know it, that's why they went out and bought all those studios to add to their first party lineup. That's why the rumor has been out that Sony is on a shopping spree for developers to boost their own 1st party lineup.
Out of the Big Three, Nintendo easily is the most fit to survive in a video game industry with no 3rd party developers. And it's not because they have the most 1st party franchises, I actually think Sony may have them beat when it comes to quantity. It's because they have consistently put themselves first and given their own franchises top priority over anything else. And that's a double-edged sword, don't get me wrong. The downside to doing that is that they have, far too many times, alienated 3rd party developers or outright burned bridges (like they did with Square Enix in the late 90s). But the upside to that is they don't become nearly as reliant on 3rd party support as Sony and Microsoft, because they bank on themselves and a "do it ourselves" mentality. As a result, they have much more direct control over their own destiny. (It also helps when the top two best selling and most popular video game franchises of all time, Mario and Pokemon, are your own IPs.) But that's the benefit of banking on yourself; Sometimes you'll fall flat on your face, but when it pays off, it REALLY pays off.
As for porting PS5/Scarlett games to Switch. That depends on the type of game, if it's something that is scaled so that it can be on as many platforms as possible, then yes, it should still happen. Anything that's taking full advantage of the PS5 and Scarlett's hardware, obviously not. Will that hurt the Switch? No, I don't think so.
The main thing when it comes to the Switch's 3rd party support in later years is that it won't get it like Sony and Microsoft are used to, but it'll get it in ways that are specifically catered to take advantage of the Switch. (i.e. Mario & Rabbids, Octopath Traveler, Marvel Ultimate Alliance 3, Bayonetta 3, SMT V.) What you need to remember about the Switch is that, moving forward (or at least in the forseeable future), it is going to be the ONLY dedicated video game system that is portable. So all of the handheld, portable, 3rd party support and games that you would see on the DS/PSP, 3DS/Vita... Especially from Japan, is all going to the Switch. Because the appeal of developing for handhelds has always been that it was significantly more affordable than consoles and the portability factor. Two core concepts the Switch will retain and should be emphasized more and more as the new gen consoles arrive and the Switch's price drops to handheld levels.
The Switch doesn't need to have the same 3rd party support as Sony and Microsoft, although it would definitely be nice to have... it needs the right 3rd party support.