I would like to pick this up. Any pointers to the best place to start would be appreciated.

This might be a particularly complicated change actually, because this type of completion would only be triggered when we don't know the name of the package so we won't have good type information. The autocompletion code can be found here: https://github.com/golang/tools/blob/master/internal/lsp/source/completion.go, but I think that you will basically need to create a case that does this here: https://github.com/golang/tools/blob/27d1b4e4f3c75e4e2c92ae1b99a67c7f34185617/internal/lsp/source/completion.go#L394, when we fail to get a package for the given file.

Change https://golang.org/cl/251160 mentions this issue: internal/lsp: add package completion suggestions