The Switch was released alongside PS4 Pro and Xbox One X so basically it's Nintendo's mid-gen refresh but unlike the latter two, it isn't sold nor share the library of the Wii U due to its lack of disc player. But it's still a mid-gen refresh

Dreamcast released alongside N64 and PS1 a full two years before the PS2 it's still considered the same gen as the latter.

I've always felt generations should be defined by time frame, so as far as I'm concerned, the Switch is Nintendo's second attempt in the 8th gen

This graph shows two different possibilities, Switch (A) would be considered 9th gen, Switch (B) however would be considered 8th gen. The Dark Blue section of the bars showing the time spent alongside the PS5/XB2. It's all down to the amount of time it spends among peers, whichever it spends more time with is where it belongs.

So it all depends on when the PS4/XBO are succeeded, and when the Switch is succeeded. Without knowing those things we can't say for definite either way.

Switch does in fact share some library with the WiiU, and it shares the hardware gimmick to some extent.  So, mid-gen upgrade seems like a reasonable position to me.  It certainly makes sense considering the launch dates of the various consoles that make up the 8th gen, and the mid-gen upgrades of its competitors.  

9th gen: Switch, PS5, Xbox4 (2017-)
8th gen: 3DS, Vita, Wii U, PS4, XOne (2011-2020?)
7th gen: DS, PSP, X360, Wii, PS3 (2004-2013)
6th gen: Dreamcast, PS2, GBA, GameCube, Xbox (1999-2006)
5th gen: 3DO, Jaguar, Saturn, PS1, N64 (1993-2001)
4th gen: NEC, Genesis, Game Boy, Game Gear, SNES, Neo Geo (1987-2001)
3rd gen: NES, Master System, Atari 7800 (1983-1990)
2nd gen: Atari 2600, Intellivision, Odyssey2, Game & Watch (1977-1984)
1st gen: Odyssey, Home Pong, Telstar, Color TV (1972-1980)

No, you're wrong. PS4 Pro was released in late 2016, the Switch in march 2017 and the One X late 2017. That's what I call "alongside".

And for the Dreamcast, 4 years after the PS1 and the Saturn isn't "alongside" to me.

Can you play wii u or 3ds games directly on Switch without a port?

No.

It remains a tough question to answer for now. I’d say it depends on how long PS4/XBOne last and how much time of Switch’s life it competes with those. If Switch overlaps with PS4/XBOne for most of it’s (relevant) life it’s an 8th Gen console. A second entry in the 8th Gen for Nintendo, because WiiU is definitely not a 7th Gen upgrade. For one because it didn’t compete with PS360, so it isn’t 7th Gen, and it’s sales aren’t counted with Wii’s because Nintendo presented it as being a successor, so it’s not an upgrade.

In Switch’s case it’s either this or PS5/XB2 should be considered 10th Gen (along with the successor of the Switch) if they take so long to release that Switch itself nears it’s twilight years, and Sony and Microsoft simply skipped a gen. None of these things are without precedent. Obviously if Switch ends up competing with PS5/XB2 in it’s adult years they’re all 9th Gen, but we simply don’t know anyone’s plans yet. Actually Barkley’s graphic above illustrates all this quite nicely.