EDIT: I'm reworking this mod, making most of the textures from scratch instead of upscaling them. I'll leave the downloads below but I'd recommend waiting until I've overhauled this overhaul.
This mod replaces almost all textures in the game with higher-quality versions, with each texture usually being anywhere from 4x to 8x larger than the original. Everything should look crisper and cleaner at high resolutions. The GUI has been redrawn from scratch to look good in widescreen, and most real-world textures (that is, textures not used in a LEGO model) have been remade with more realistic graphics. LEGO textures were put through a kind of vector upscaler, due to the simple graphics, and hence you'll see some parts are rounded so I might come back and clean them up another day. The only textures that haven't been edited are cursors, which don't scale, and fonts. Also the LMap.pac file was left alone as there is some crazy junk in there.
Download
Warning - this is a 520MB download, which uncompressed hits around 1GB. You'll need enough RAM to load that, and may notice loading screens being a tad slower than usual.
Google Drive
Mega
Installation
If you have LEGO Alpha Team installed, see @lordtobi's post here to set it up for custom resolutions including widescreen.
If you don't have LEGO Alpha Team installed, check out the Windows 10 installation tutorial here.
Go into the game's install folder, which for me is C:\Program Files (x86)\LEGO Media\Games\LEGO Alpha Team, and create a new folder called "Original PACs" or something to that effect. Move the game's original Map.pac and Etc.pac files into this folder, so that they are no longer present in the same folder as the game's install files and you have them as backups to easily restore. Now extract the Map.pac and Etc.pac files from the downloaded ZIP file and move them into the install folder. Launch the game as usual and enjoy the mod!
Previews
Check out previews of the mod here. I recommend you open them in a new tab and flick between the two for comparison.
Splash Screen
The main level is too zoomed out, but notice the new "Alpha Team" logo and water.
Main Menu
Earth uses textures from NASA, I redrew TeeVee's screen from scratch, and you can see the new widescreen HUD too. For some reason TeeVee's antennae always look somewhat pixellated, even though they're currently smooth at 1024x1024 resolution.
Game
Here you can see substituted textures for the real-world elements, as well as the smoother LEGO parts such as the text on the studs.