Convert `public-bg.png` to modern image formats (AVIF/WebP)

[spli02]

The PublicLayout component currently uses a PNG image located at src/assets/images/public-bg.png.
To improve loading performance and reduce image size, this image should be converted to modern formats such as AVIF or WebP.
(Consider using a combination of both formats, serving AVIF to browsers that support it and falling back to WebP for others.)

Ref: https://cloudinary.com/guides/image-formats/avif-vs-webp-4-key-differences-and-how-to-choose