Do I need Loopback or Mixline to visualize Spotify with SYQEL?

With SYQEL Desktop, no. Play something in Spotify, then pick App Audio: Spotify in the audio source list at the left of the top bar. This needs macOS 14.4 or later, or Windows 10 build 19041 or later. See How to visualize Spotify music with SYQEL.

In the web app, or on an older system, yes, you need a virtual audio device. A browser can only hear a microphone or an audio input, not Spotify or another tab. Loopback and BlackHole work on a Mac, and VB-Cable on Windows. See Creating a virtual audio input.