x/pkgsite: search page redesign #47321

This is the umbrella issue for an upcoming redesign of the search page on pkg.go.dev. Specific plans will be discussed via the issues below:

• x/pkgsite: group search by module #47320
  • Includes x/pkgsite: grouped search fails to group some modules #47839
• x/pkgsite: pageless search #47315
• x/pkgsite: support searching by <package>.<identifier> #44142
• x/pkgsite: search shortcut key doesn't work consistently across site #42704

The motivation for these changes were originally discussed in #41585.

Copied from the "Search page" section:

Search results are noisy:

• x/pkgsite: do not show packages of a module at the top level #37788
• x/pkgsite: searching for modules isn't supported #36814
• x/pkgsite: searching for "youtube" only show results for github.com/youtube/vitess  #39525

The “latest” version for a search result can be confusing:

• x/pkgsite: search ranking ought to prioritize more recent major module versions #36969
• x/pkgsite: search results show incorrect latest version if the latest version of the module and package do not match #41108
• x/pkgsite: partial search doesn't return (any) matches which are "close" or latest #36806 (comment)