A genuine question: if the Switch surpasses the PS2, can it be considered the best-selling home console of all time, or will we have to disregard the Switch Lite's sales figures?

People still debate if Switch is 8th gen, 9th gen, or both.

So, the debate you mention will likely also continue. 

Well, it passes 160M when Nintendo wants it to - if it wants to. I would guess they could sell Switch or Lite for 99 or so to push beyond whatever they want to. A Switch Pocket for 69€ and sell 20 million of those.

Does the 160M number for the PS2 include the consoles solely being bought as a DVD player or not ?

Looks like the first part of my prediction last November is assured but the second will likely slip a month or two.  I do think Switch will pass 156m by the end of March like Nintendo predicts.  However, the last part of my prediction definitely ain't happening.  I voted for end of 2028.

The Switch 1 price hikes have certainly had an effect on this goal, making the original and OLED models look bad value-wise when compared to just buying a Switch 2.  But the Switch hitting 160m was always going to come down to the Switch Lite's affordability and that hasn't changed that much.  The market for budget gaming may be small but is sustained by casual users, kids... people who would buy a 3DS for half the price of a brand new Nintendo Switch in 2017, for example.  And keep in mind that the 3DS still sold around 9m after the release of the Switch.  The Switch is far more saturated though and may be tracking lower when aligned after a successor's release, but it has a far stronger library than 3DS ever did and not as far to go.  Plus, Switch has transferable accounts and games for anyone ever looking to upgrade to the Switch 2 family, making its forward compatibility an asset of its worth.

So there is still a lot of value in the Switch Lite as the affordable Nintendo handheld until a Switch 2 Lite model releases, which would likely be late 2027 if history repeats itself.  And the 3DS was discontinued a year after Switch Lite arrived.  So will the Switch Lite's affordability and longevity in Japan be enough for 4m more from April of 2026 until mid-to-late 2028 when it ends production?  It's going to be close either way, but I wouldn't count it out just yet.

Still predicting 159m - 161m LTD 

But is there any PS2 model that officially functioned only as a DVD player?

Most stupid discussions of all time!

I think it's impossible to know the number of people who bought the PS2 solely for its DVD player function; the same applies to people who bought a Switch for another purpose. Now it's easy to distinguish between Switch and Switch Lite. Conceptually, the Lite is clearly not a home console.

So I think if the Switch surpasses the PS2, this discussion will get heated.

It includes even the systems sold to Iraq for missile guidance systems. 

The biggest reason this is very unlikely to happen at this point is the Switch post Switch 2 is selling worse than the DS did post 3DS so far when it needs to be doing better. The DS was at 151.52m shipped by the end of March 2012 and only shipped another 2.5m after that so assuming the Switch is at 156-156.5m by the end of March next year it has to suddenly go from doing worse to doing significantly better than the DS post successor to reach 160m.

That happening isn't impossible since Nintendo could do the surprising move of releasing a final revision next year but with them clearly not showing interest in continuing to push Switch 1 hardware sales I really doubt that'll happen and it wouldn't release till April at the earliest so it's questionable if it would even help enough to make it possible. Either way things need to change fast or else the Switch getting to 160m will become impossible soon.