Lifetime? Not a chance. The way things are going, PS5 will tap out at ~ 105 - 110 million lifetime through EOY 2028, and that's assuming there aren't other price increases to come, that GTA6 is the "industry savior" as analysts want to frame it, and SIE doesn't do Day 1 for the big games to PC (Steam) prior to that.
Otherwise, and especially if all three things happen (in the case of GTA6, it'd mean the game underperforming by a decent margin, say 20%-30%), then lifetime PS5 sales could tap out at just 100-105 million. I mean look at it this way; sales are already tracking behind PS4 launch-aligned, they've been 2 million behind PS4 launch-aligned globally, and they've been pushing aggressive sales promos in Europe because that's one of the territories sales have softened more than expected.
I also don't think markets like China are going to be a massive boon to PS5 as some believe, because as long games like BMW are Day 1 on PC, a market whose gaming audience overwhelmingly favors PC, will just go PC for those games. Plus how many more BMWs are SIE expecting over the next four years?
The thing you're ignoring here, is that PS5 had a much faster start than PS4, so a lot of SIE's early FY projections (before revisions) assumed that momentum would stick around. Now yes, COVID and the pandemic, alongside chip shortages, happened, and those things affected SIE's ability to satisfy demand via supply.
But that's also around the time SIE started to self-sabotage their hardware demand with both aggressive cross-gen support (HFW, GT7, GOW Ragnarok) and an intensification of their Steam porting strategy to PC (Returnal, GOT, DS: Director's Cut etc.). The fact of the matter is this: as Xbox has seen a massive collapse in console sales globally, by all accounts most of those gains should have been going to PS5.
However, it'd appear a majority of the deserting Xbox customer base, have chosen to turn to PC instead, which would explain the increase in Steam growth specifically (and other things like PC"s market share growth in Japan) while PS5 has remained virtually stagnant with PS4 and is now trailing them behind by some 2 million globally. IMO, if SIE didn't go for the easy bait, and didn't self-sabotage vested interests in their console, PS5 would've been able to maintain the pent-up demand it had during lockdowns longer and would be at least slightly ahead of PS4 globally when launch-aligned. Especially, again, considering the fallout that's happened with Xbox this gen.
Also in terms of comparing PS5's LTD to Switch's, you are ignoring that Switch was VERY under-supplied in the first year or so. It had a somewhat similar issue in terms of low supply relative demand, that PS5 had in 2021 and most of 2022. Had Switch satisfied that demand earlier on, I feel LTD amounts would put it decently higher than where it's already at relative PS5, because Nintendo hasn't engaged in the sort of self-sabotaging strategies (or better to say, methods of implementation of the strategies) the way SIE has with PlayStation.