dev env: Change app deployment script to use gh-pages

[OleksiyRudenko]

Issue 1

Problem:
a8e06ad (currently on dev) brings back push-dir as a publishing script.
Alternative deployment package gh-pages is already listed among dev dependencies.

Desired outcome:
gh-pages is used as a publishing method.

Suggested approach:
package.json: change deploy script so that it runs gh-pages -d dist

Issue 2

Problem:
a8e06ad (currently on dev) brings back shell interpretation of glob passed to npx prettier.

Desired outcome:
npx prettier glob is quoted and therefore interpreted by prettier, not shell.

Suggested approach:
package.json: change prettify script so that it runs npx prettier --write \"**/*.{js,css,md,html}\"

[m-shulipa]

This would change only package.json so I think it'd be safe to make PR and merge to dev