The original AC Adapter is only good for charging, not for playing on TV.
http://www.nintendoworldreport.com/news/70558/full-list-of-nintendo-switch-accessories-not-compatible-with-switch-2-revealed
Nintendo has just revealed a comprehensive list of which Nintendo Switch Accessories are not compatible, or only have limited compatibility, with the Switch 2 system.
Notably, the original Switch AC Adapter can charge the Switch 2 when connected directly, but cannot power the system via its new dock to play in TV mode due to "differing power output."
Unsurprisingly, the original Switch dock is NOT compatible, as the Switch 2 dock seems to be uniquely made for the newer system. Neither is the original HDMI cable included with previous systems compatible with the Switch 2 due to different HDMI cable standards for the new console.
Original Joy-Con controllers and Pro Controllers are considered compatible and can be connected wirelessly.
The official Gamecube Controller Adapter is compatible.
Specialty classic-style controllers like the NES, SNES, and N64 controller are considered compatible, but include an asterisk that they work with compatible games.
For a full list of which official accessories are compatible, click here.