First-party/Third-party software split depends on a per-platform basis (how much third-party support a console receives).
In Japan looking at the packaged software sales in the annual top 1000 by Media Create since the mid-'00s, it could be generalized saying that SCE/SIE's first-party software tends to be around 10% whereas Nintendo's first-party (Nintendo+Pokemon Co) software has usually the majority of the sales.

First-party/Third-party packaged software split in Japan for specific platforms:

NDS (miss 2004 and 2005)
First-party: 52%
Third-party: 48%

PSP (miss 2004 and 2005)
First-party: 6%
Third-party: 94%

WII
First-party: 74%
Third-party: 26%

PS3
First-party: 10%
Third-party: 90%

3DS
First-party: 43%
Third-party: 57%

PSV
First-party: 12%
Third-party: 88%

WIU
First-party: 82%
Third-party: 18%

PS4 (as 2020)
First-party: 16%
Third-party: 84%

NSW (as 2020)
First-party: 69%
Third-party: 31%

PS5 (as 2020)
First-party: 69%
Third-party: 31%

PS5 in 2020 was the first time since 2006 that a PlayStation console had more first-party sales than third-party sales at a certain point in time. It demonstrates the decline of Sony in Japanese territory. Sony was a third party driven

Source: InstalBase (thanks Celine)

Not to mention a lot of games already have either skipped playstation or gone multiplat
The atelier games and trials of cold steel moved to switch after years of being "only on playstation".

octopath traveller, triangle strategy, no more heroes 3 and MHR skipped playstation

And lets not forget about the meltdown sony fans had when disgeia 6 skipped playstation (in the west)
Sure the big devs won't abandon playstation, but there are lots and LOTS of other devs that are considering switch only titles despite playstations worldwide "dominance"

Some games that were initially announced as PS only had announcements to go to multiple platforms. Demon Slayer was initially announced as PS4 only. What's funny is Trails of Cold Steel 3 was PS4 only and has the "only on Playstation" on the case, then a month after it's release in the West a Switch version was announced, then another month later a PC version got announced. Just recently Grandblue Re:Link announced it would no longer be PS4/5 only, it's now going to PC. 

Funnily enough for NIS America they probably will not publish a game in the West unless there is a Switch version. Like seriously, go look at their past and upcoming releases. Almost all of Koei Tecmo's games since the Switch launched are on Switch. The 2 games since it's launch that aren't on there are Dynasty Warriors 9 and Nioh 2. Let's not forget the Tale of games. Vesperia DE went to all 4 platforms and Arise went to 3.

People need to accept the era of exclusives are over. Games that were PS only now include PC, Xbox, and/or Switch. 

basically going foward, japanese devs would likely develop switch as a base platform then just scale up resolution for a ps4 realese.

in fact, i can actually see quite a few japanese devs not develop for the PS5 at all in this case, since ps5 can play ps4 games anyway. they'll just go ps4/switch untill switch sucessor drops and it outpreforms ps4. mostly casue 4k development is freaking expensive, thats the main reason most japanses devs jumped from ps2 to psp instead of ps3.

No it isn't.

Switch is significantly more capable than any 7th generation console.

There is room to do well both in Japan and the rest of the world. Unfortunately, Sony doesn’t seem to think that way.

The Switch shows you can do just that. It’s not only dominating Japan, but it’s doing well everywhere else. Nintendo is dominant in East Asia outside of Japan. It set a record for most consecutive months of being the best selling console in the US. In Europe, Nintendo has seen improvement in sales compared to previous gens. The week of November 22 was recently Nintendo’s best week in Europe.

https://www.google.com/amp/s/www.eurogamer.net/amp/2021-12-10-nintendo-switch-had-best-ever-week-in-europe-last-month

How is Nintendo able to sell well EVERYWHERE (including Japan) but Sony isn’t able to the same despite having more resources and third parties supporting them than Nintendo?

Yeah, well, that is the result of people believing their own propaganda. If Wii is barely able to match a PS2 and WiiU does not really improve on Wii and Switch basically does the same as WiiU, if you believe all this, then the Switch *must* be two gens behind.

But the reality is people forgot how PS3 and X360 games looked like. The WiiU did already more than that and Switch improved further upon that as illustrated by the WiiU ports.

The real takeway from this week for PS5 isn't that it has stock shortages because it has to be expected, it's that SIE allocated at most 1.9K for Japan in a week in the most important shopping period of the year.
That's how much confidence SIE have in the japanese market.

And as a result it will shape what confidence japanese devs and customers have in the PS ecosystem.

It’s probably been posted early in the thread, but I will be excited when Famitsu announce Animal Crossing has sold 7 million copies in Japan at retail very soon.

In an era where there’s probably a couple of million digital sales as well it’s amazing to see a juggernaut up at the level of Pokémon games with three or four versions.