OK after sleeping, I realized what your issue probably is.

So by default, in the Steam Properties for a game, the resolution is set to “Default”. So when you plug it in to and display on an external monitor like a 1080p one, it uses the closest appropriate resolution to the steam deck’s display (1280x800) but with the new ratio (which is 16:9, as your external display). This is 1280x720; ie. 720p.

What will happen then is the Steam Deck will use the built-in OS scaling method, to upscale this from 720p to 1080p. In your side performance menu (the button with the “…”), you can set this to FSR with a Sharpness of about 2 to make it looks better. The issue with this method is that everything is using upscaling, including the UI; which makes everything a bit blurry.

But you can also instead do it another way, which is to force the game to launch at 1080p, and use the in-game FSR2 so that only the 3d game engine will use upscaling and the UI will be sharper.

• In Steam Properties, set the Resolution selection to “Native”; this will launch the game and allow for it to see the native resolution of the display you’re using, whatever that is (Steam Deck or the external one).
• After Launching Baldur’s Gate 3, go into the game settings, use Windowed Fullscreen (this will use whatever resolution the full screen window is at; so 1280 on your steam deck and 1920 on your external display), and then set FSR2 to ON with Performance or Quality setting. Also put the Sharpness Slider about 80%.

So the above setting should run the game in a manner where the UI looks sharp, and you still get performance similar to when you run it on your steam deck native screen.