The first shot was inspired by the aesthetics of Y2K futurism, an early 2000s retro style born from the techno optimism of it's time. The background uses multiple layers using turbulent noise and wave warp to achieve a pool-like look. A layer of deep glow and contrast was used to give it a more ethereal look.
For the disk, I used an expression to randomize the colors to produce multiple variations. The disc I chose eventually shaped the overall color scheme for the rest of the intro.
Shot 2 uses a bunch of techniques and tricks for each rectangle, including expressions and effects. Going over each one could take awhile, so I may make a separate post going over each part.
Shot 3 utilizes both After Effects and Blender. The tunnel and trail following the star was made using Blender geometry nodes, while the colors and compositing used the Colorama and Deep Glow effects. The star itself is a shape layer in AE, but parented to a null animated and exported out of Blender.