Cannot start Nuxt with new Tailwind version

[tsiotska]

v4.0.1 -v4.0.3 (compatible with prev versions e.g. 3.)
NUXT 3.15.2
Node v20.12.2
@nuxtjs/tailwindcss: "^6.13.1",

I am not sure If issue refers to tailwind, I just downgraded to 3.4.17 and don't see message below anymore:

ERROR Cannot start nuxt: It looks like you're trying to use tailwindcss directly as a PostCSS plugin. The PostCSS plugin has moved to a separate package, so to continue using Tailwind CSS with PostCSS you'll need to install @tailwindcss/postcss and update your PostCSS configuration.

Yes, I tried to install plugin and update postcss, it's just not the way it gotta work and indeed it doesn't. If anyone interested please take a better look than I did. :)