You can definitely play with your original Switch cartridges on Switch 2
While backwards compatibility was confirmed in November, we didn't know if physical media would be supported

Before the reveal of the Nintendo Switch 2 design we already knew that the console would be backwards compatible with old Switch games in some way.
That was thanks to a November 2024 statement from Nintendo president Shuntaro Furukawa that was posted to social late last year: “Nintendo Switch software will also be playable on the successor to Nintendo Switch”. But while backwards compatibility was confirmed, what we didn’t know was whether the console would support physical media as well as digital.
The Switch 2 was revealed back in mid-January and the accompanying video revealed just how backwards compatible Switch 2 is: the new console supports the insertion of physical carts and Nintendo said at the time that the new console would “play Nintendo Switch 2 exclusive games as well as Nintendo Switch games”.
However, the ruling won’t apply to every Switch game ever; Nintendo notes that “certain Nintendo Switch games may not be supported on or fully compatible with Nintendo Switch 2” with details on which titles are affected to appear on Nintendo’s site in the future. So we don’t yet know what games those will be. However, they seem certain to be in the minority and we’d expect them to be more niche titles.
We also know that Nintendo Switch Online will also be seamlessly available on the new device (as you’d expect).
Backwards compatibility isn’t always available when new consoles are launched, of course, While it’s pretty much unthinkable that Nintendo wouldn’t make the Switch 1 and Switch OLED games compatible with Switch 2, the Wii U wasn’t compatible with the Switch for example and neither was the Nintendo 64.
Check out our previous opinion piece on this topic: I hope Nintendo Switch 2 loves old game cartridges, not just old games