This is a tracking issue for the implementation of #44542

• DB backend and GraphQL API for setting starred and default context (search contexts: backend for setting as default and starring #44624)
• Remove auto-defined contexts from the frontend, add global context to the existing search_contexts database table (search contexts: remove autodefined contexts from frontend, add to normal query #44875)
• Modify GraphQL API query for SearchContexts to return in new order: first default, then starred, then any other contexts (search contexts: order contexts list by default first, then starred, then others #44876)
• Implement new design for search context management page with table and menu
  • Update page header (search contexts: update header in list page #44966)
  • Use table view for desktop mode (search contexts: table view in management page #45001)
  • Use cards for mobile/tablet mode (search contexts: card view for mobile #45040)
• Enable search context management page for everyone (search contexts: permanently enable management page #45302)
• Implement stars
  • Implement adding/removing stars in search context management page (search contexts: add support for starring and unstarring contexts #45230)
  • Implement adding/removing stars in individual search context page (search contexts: allow starring from the individual context page #45281)
  • Show stars in search context dropdown (search contexts: show stars in search context dropdown menu #45289)
• Implement default context
  • Implement setting default context in search context management page (search contexts: allow setting a default context and use it on load #45387)
  • Implement settings default context in individual search context page (search contexts: set default from individual page #45391)
  • Show default context in search context dropdown and remove the Reset button (search contexts: show default context in dropdown #45430)
  • Add backend to query default context (search contexts: add backend for querying default search context #45483)
  • Modify search context behavior so default context is always selected first when the page is loaded. Remove the use of LAST_SEARCH_CONTEXT_KEY item in localStorage. (search contexts: select default context on page load #45489)
  • If no default context is available, a notice is shown in the dropdown to prompt users to select a new default. (search contexts: show alert if default is not available #45500)
• Add docs (docs: add search contexts starring/default and fix inconsistent links #45569)

Post-implementation cleanup and polish (not necessary to complete this issue, can be spun off later):

• Implement page-based pagination in search context management page (depends on Add usePageSwitcherPagination hook #44664)
• Completely remove auto-defined contexts from GraphQL API and backend
• Add action to duplicate a context (RFE: Button to Duplicate Search Context #44670)

/cc @sourcegraph/search-product