How can I make sure my video renders don't have that weird color and texture vibration? Check outref

  1. How can I prevent my video renders from having strange color and texture vibrations?
  2. I’ve tried adjusting different settings, but the issue persists.
  3. Can anyone offer any solutions or advice to resolve this problem?

I hope this helps. If you need anything else, feel free to ask!
Render video, demostration

Increase your number of samples when rendering.

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But what would be the optimal number for, let’s say, a full HD video to stop lagging? On the other hand, it could also be a texture issue, sometimes it appears like that, other times the render turns out fine.

Color Management’s filmic can be helpful for color issues.
Color Management — Blender Manual

The problem with texture is noise patterns (removed by Denoise)
Increasing the sample value will improve to some extent.
The appropriate sample value is not known because it depends on the scene configuration.

Optimizing Renders — Blender Manual