Nintendo Switch 2 will be very similar to Nintendo Switch, but also a big departure: the console itself is larger, and has different, magnetic Joy-Cons (called Joy-Cons 2) that will be used for the new games. However, it has been confirmed that it will be backwards compatible with most of the games - the only game NOT compatible is Nintendo Labo Toy Con 4: VR.
"If you have Nintendo Switch Joy-Con controllers and connect them wirelessly to Nintendo Switch 2, you can play these games as you would on Nintendo Switch". That includes titles that used the Joy-Cons a lot, like Ring Fit Adventure (Joy-Cons 2 do not fit on the Ring-Con), 1-2-Switch, Everybody 1-2-Switch!, Game Builder Garage, WarioWare: Move It!, or Switch Sports.
This means that, yes, Joy-Cons from the original Switch will be compatible with Switch 2. However, because the console itself is different, they will only work wirelessly. Nintendo confirmed it on their website: "A Nintendo Switch console or an accessory such as a Joy-Con charging grip or Joy-Con charging stand is required to charge Nintendo Switch Joy-Con".
It is also confirmed that the Pro Controller from Switch 1 will also work on Switch 2 if you want to play multiplayer on local games like Mario Kart, Mario Bros. Wonder or Super Smash Bros. Ultimate. Nintendo will launch a new Pro Controller 2 for Switch 2 (won't work on Switch 1) and it will be improved and more expensive...
However, we do know that, despite the Joy-Cons 2 having upgrades like the "Mouse control", it will lose one of the weirdest features of the first Switch: the IR Motion Camera on the right Joy-Cons, so some minigames from 1-2-Switch and its sequel, as well as Game Builder Garage and WarioWare: Move It! will not work.
What is more, it seems that Joy-Cons 2 will lose some of the intensity of the vibration. For Everybody 1-2-Switch!, Nintendo said that "The volume of the Joy-Con 2 controllers' force feedback vibrations has been reduced compared to the Nintendo Switch Joy-Con controllers, so it may be more difficult to find hidden Joy-Con 2 in the minigame Joy-Con Hide & Seek."
Nintendo didn't highlight HD rumble or any type of haptic feedback on their trailer. We know that they will have HD rumble similar to the Joy-Cons from Switch 1, but it may have lost some power... although not many games really used it to their full capacity.