Persist homepage activity feed filters

What does this MR do and why?

What

Persist homepage activity feed filters

Why

As requested: When a user returns to the homepage, default to the activity feed mode that was most recently used

References

Screenshots or screen recordings

How to set up and validate locally

1. Enable feature flag personal_homepage (gdk rails c -> Feature.enable(:personal_homepage))
2. Navigate to the home page from any user (top item in left sidebar)
3. Change the activity filter to a different filter
4. Reload the page (or navigate to another page and come back to the home page)
5. Observe that filter has been persisted

MR acceptance checklist

Evaluate this MR against the MR acceptance checklist. It helps you analyze changes to reduce risks in quality, performance, reliability, security, and maintainability.

Related to #545444 (closed)