[Infra] Replace storybook-deployer with github-actions-storybook-to-github-pages

[mdeliatf]

Feature request

Overview

While working on #426 and #427 I've noticed We are publishing the Storybook app using @storybook/storybook-deployer.
This project's been archived and forces the usage of npm - not a big problem for us, since the library is still built using yarn, but still a little inconsistency.
Another modern solution, supporting yarn, is available as suggested in the Storybook documentation - please see the link below.

Examples in other libraries

Please see https://storybook.js.org/docs/sharing/publish-storybook#github-pages.

Who does this impact? Who is this for?

Faency maintainers/developers.