Animal Crossing New Horizons – Items Sold in Nook’s Cranny Front Corner: Comprehensive Overview

If you buy a second Switch, you're no longer sharing the same island. There is no cloud save transfer available for the game. There will be a data recovery service available later, but it doesn't sound like it can be used to keep an island in sync between two Switches.

Each Switch will have its own island. You can use local or online multiplayer to visit the other player's island or have them visit yours to play together on separate screens.

https://www.ign.com/wikis/animal-crossing-new-horizons/How_to_Play_Multiplayer#Local_Wireless_and_Online_Multiplayer

I have seen the future and the past. I have time traveled for hundreds of years (by adjusting my Switch system clock) and this is what I learned:

• There is no major effect. No nagging, no obvious penalties, despite what IGN said. Indeed, on the plus side, progressing into the future earns interest on your Nook Bank balance (in the ATM/ADM), maxing out at 99k bells at a time.
• No residents left town, in my case. Caveat emptor: I did this before actively recruiting new townspeople. For what it's worth, I ignored townspeople when I time traveled (man on a mission), which might have stopped the game from registering that I had "ignored" the residents. For example, if I progress into the future and talked to a resident, they'll remember that it's been weeks/months/longer since we last spoke, but once I returned into the past and talked with the residents, they wouldn't say anything about the time passed.
• I also didn't especially notice more weeds or anything falling into disarray, but that might have been because I traveled between winters, when snow covered the ground.
• Not specific to time travel but to putting down the game in general, if you haven't been "in-game" in a while, there may be changes that are not recapped in Isabelle's morning announcement, such as new residents who came and were ostensibly announced while you were gone.