docs(fix): persist tabs state (#10313)
### Description
Fixes bug where package manager tabs weren't persisting or sharing their
state. Also deletes some unused code that used to be for this purpose.
### Testing Instructions
Visit
https://turbo-site-git-shew-441a4.vercel.sh/docs/getting-started/installation
and notice how the two package manager tabs are always in sync. You can
also refresh and your selection will stay.
