[Documentation]: Update docs site to remember the selected package manager

[ChristopherHaws]

Describe the problem

I am looking through the docs quite a bit right now since I am new to storybook and I am using pnpm as my package manager. Currently in the docs site when you select your package manager for a script, it only changes the selected package manager for that single code snippet and refreshing the page forgets the selection.

I think it would be a better user experience if changing the package manager anywhere on the docs site would store a config in local storage or a cookie and triggered all of the code snippets to change to the selected package manager.

Additional context

Here is a screenshot of me selecting PNPM for the first code snipped, but the second one didn't automatically change so it is still showing the NPM script:

[jonniebigodes]

@ChristopherHaws thanks for taking the time to open up this issue and letting us know of this issue. We appreciate it. But If you're ok with it, I'm going to transfer this to the frontpage repository as it's where the website is located and ping one of my fellow team members to follow up with you when able and see how best to address this issue. Sounds good?

cc @kylegach

Hope you have a great day.

Stay safe