I’ve marked this as broken for now. @angus please feel free to remove the tag if/when it’s been updated.
As well as the deprecations, core’s search implementation recently switched from Widgets to Glimmer Components, so I imagine this theme would need significant refactoring to get it up-and-running again.
As @Arkshine said, we have a couple of similar official theme components, so they are a good alternative (or a good reference on how to re-implement this one)