Well, you say it yourself, the generations don't line up. Therefore I see not much sense in declaring Switch in the same gen as PS4 or PS5. If we assume PS4 and Switch both follow a normal console-lifecycle, then Switch will be 2.5 years on market with PS4and 3.5 years with PS5. Declaring it to be in the same generation as either of them is illogical. As far as we know, both could deviate from the lifecylce again and making the differences even bigger.
Also Nintendo did deviate earlier, the GBA had only 3.5 years as the DS came out.
Much of this is similar to 2011 when many people had a hard time accepting that the 3DS was 8th gen. What was certain back then as it is now is that the 3DS was not part of the same generation as the DS, just like Switch is not part of the same generation as the 3DS.
Nintendo also deviated with the GB which went on for nine years before the GBC hit the scene. Still, GB + GBC ended up at twelve years, so the duration of two generations. The GBA was cut short because Sony wanted to get a headstart with the PSP over Nintendo's next handheld.
I personally consider PS4, Xbox ONE and Wii U as 8th Gen, and PS4 Pro, Xbox ONE X and Switch as Gen 8.5
There where such interludes before. In between 4th and 5th gen with Philips CDi, 3DO, Amiga CD32, and you could also count Sega's X32 and NECs SuperGraphX to this. The Atari 5200 could be seen as Gen 2.5 considering how quickly it got replaced by the 7800, too. Upgrades within a generation are not new, just very seldom used.
That isn't any better than calling Switch 8th gen, because you categorize Switch as mid-gen upgrade when it is clearly next generation, unlike PS4 Pro and Xbox One X.
Software sales after 3 quarters: (Attach rate in parentheses)
GBA: 21.80M (2.28)
GCN: 14.37M (4.25)
DS: 15.82M (2.38)
Wii: 44.82M (4.83)
3DS: 17.56M (2.63)
WiiU: 14.44M (4.00)
Switch: 27.48M (3.60)
Switch has a higher attach rate than all of the handhelds, but a lower attach rate than all of the home consoles.
However, bundled software is counted in these numbers: Wii Sports inflates the Wii's attach rate by at least 0.8, and Nintendo Land has a similar effect on Wii U. Not to mention how GameCube, Wii, and Wii U all went through a holiday season in this period, while Switch did not.
For reference, Wii sold 15.98 million units of software in its second and third quarters (Jan-June 2007), while Switch sold 22.02 million units of software in that period (Apr-Sep 2017).
Wii's attach rate is certainly not inflated by at least 0.8 when Wii Sports was the biggest reason why people bought the system. Wii Sports wasn't a bundled game that nobody wanted.
If you want to spin this to make Switch look better, simply point out that Switch's digital business is much bigger than any of the previous consoles'. Nintendo's software figures only count digital sales for titles that are available at retail, so digital-only games are excluded from the totals.