PS1 sold 962 million software and PS3 1 billion, so Switch should pass both of them this quarter.

I can't find software totals for the Xbox consoles, anyone have those?

Xbox 360 was over 1 billion. It was the console with the highest software sales of the 7th gen.

The mark to beat is the PS4 SW, which is about 1.6-1.7 billion units, and still selling,  (the last official number was 1.577 billion in April 2021).

So PS4 has the lead for most software sold? I was under the impression that was PS2

Yes, it is the PS4, but Switch will definitely be Top 3.

Time will tell which position. 

With Pokemon Scarlet/Violet probably selling close to 20 million on it's own in Q3 the Switch has a good chance of breaking Nintendo's Q3 software record.

Nintendo Software FYQ3 (Oct 1 -Dec 31) 

1. NSW - 85.40 million - 2021

2. Wii - 85.33 million - 2010

3. Wii - 82.37 million - 2008

4. Wii - 80.43 million - 2009

5. NDS - 78.76 million - 2008

6. NSW - 75.85 million - 2020  

7. NDS - 71.39 million - 2007

8. NSW - 64.64 million - 2019

#3 of all time in both software and hardware at the end of its run seems a fairly safe bet then.
In both cases, this is the quarter where it will move multiple ranks up the ladder.

Still incredible that this generation follows on from both their worst selling console and handheld. Not even going from the Gamecube to the Wii was this much of a turnaround.

Discounting the few loons who say that [insert console name here] will end up being the biggest selling console ever in the usual VGChartz poll and discussion that happens prior to each new consoles launch, it can be said that even those of us who were optimistic never saw this scale of success.

While the Switch was coming after the Wii U with it's poor sales, because it was essentially combining both of Nintendo's gaming sides into one most logical people saw it as a positive move that would easily surpass the Wii U.

What was undecided was exactly how much of a success the Switch would be when put up against the combined 3Ds and Wii U then questions like with the exception of the Wii, Nintendo home consoles hardware sales historically aren't that big so how much growth would have to come from the handheld side and if so would it have the software attachment ratio of a handheld or be more inline with the higher ratio of a home console, now these questions were answered in the positive when early in the piece it became obvious that the Switch's impact was far more than what you would expect from the sum of the parts it replaced, but even following all that early success that quickly evolved from us talking about would the switch succeed into talk about the Switch matching or passing the Wii, who would have imagined that a few years later the scale of those covid year sales has meant that in 2022 its no longer about matching the Wii but the PS2.

Pretty much, yeah, outside of those usual few shoot-for-the-sun claims, the idea that the Switch would so this well was considered an insane pipe dream prior to its launch, and even in its early life.

Heck, back in 2017 and 2018 a lot of folks still thought it would sell less than the 3DS, and when Nintendo announced that they were aiming for Wii level sales, most people scoffed at the thought and said it would never happen.

Imagine going back and forecasting it would outsell the PS4 back in 2016 or 2017, you'd be labeled a delusional fanboy. And yet, here we are.

I always believed Switch would do at least Wii U/3DS combined numbers with the chance to outsell the Wii. That being said, I thought those things would occur near the end of its life. It actually occurred less than 5 year after launch with a couple more decent years still to go! It is true that Switch has blown past even the most optimistic expectations.