Hi there, I'm Matt Sergei (do call me Matt, please) and can create your website loading animation.
The animation in your referenced video was created using video software and exported to a GIF and that is not smart e.g. 1+ MB for such animations as it has to download, initialize etc - while user is waiting.
My bid is for SVG standalone (possibly javascript supported) with this idea:
1. Yellow square appears and creates a blue drop first by circling around it (from the bottom anti-clockwise).
2. Then it creates a red/purple dot the same way, continuing moving anti-clockwise.
3. When a square passes a bottom of the blue drop and moves up right a white circle appears (fades in or drops in by zooming out) in the center of a blue drop.
4. A square is stunned and pushes a circle down left and moves over blue drop to its final position.
5. A circle bounces a few times inside the red/purple dot.
6. When a circle settles the "AUTOVAY" caption fades in, revealing letters to right.
7. The whole scene fades out after a pause and starts over.
My bid is final because I'm incorporated, 3/4 of my minimum daily rate (6 hours is estimated to vectorize, draw all paths, including invisible ones for a square and a circle, and animate all).
The deliverables will be SVG + javascript (with minimal GreenSock javascript library, preferred) or pure standalone SVG with embedded animations (harder to implement).
Please do not accept this bid before Friday.
Best Regards and hope you are safe,
Matt