cmd/go/internal/vcs: use git log to avoid unnecessary objects

"git show" by default shows the diff from the previous commit. "-s"
suppress all output from the diff machinery. But it will still try to
fetch the relevant objects, which may be unavailable if the repository
is a partial clone.

Use "git log" instead, which only needs the commit object.

Fixes golang#65339

src/cmd/go/internal/vcs/vcs.go

@@ -331,12 +331,12 @@ func gitStatus(vcsGit *Cmd, rootDir string) (Status, error) {
 	}
 	uncommitted := len(out) > 0
 
-	// "git status" works for empty repositories, but "git show" does not.
-	// Assume there are no commits in the repo when "git show" fails with
+	// "git status" works for empty repositories, but "git log" does not.
+	// Assume there are no commits in the repo when "git log" fails with
 	// uncommitted files and skip tagging revision / committime.
 	var rev string
 	var commitTime time.Time
-	out, err = vcsGit.runOutputVerboseOnly(rootDir, "-c log.showsignature=false show -s --format=%H:%ct")
+	out, err = vcsGit.runOutputVerboseOnly(rootDir, "-c log.showsignature=false log -1 --format=%H:%ct")
 	if err != nil && !uncommitted {
 		return Status{}, err
 	} else if err == nil {

src/cmd/go/testdata/script/build_git_missing_tree.txt

@@ -0,0 +1,49 @@
+# Regression test for https://go.dev/issue/65339.
+# Unnecessary git tree object required
+
+[short] skip 'constructs a local git repo'
+[!git] skip
+
+env GIT_AUTHOR_NAME='Go Gopher'
+env GIT_AUTHOR_EMAIL='gopher@golang.org'
+env GIT_COMMITTER_NAME=$GIT_AUTHOR_NAME
+env GIT_COMMITTER_EMAIL=$GIT_AUTHOR_EMAIL
+
+# Create 2 commit
+env GIT_COMMITTER_DATE 2024-01-30T10:52:00+08:00
+env GIT_AUTHOR_DATE 2024-01-30T10:52:00+08:00
+
+cd $WORK/repo
+exec git init
+exec git add go.mod main.go
+exec git commit -m 'initial commit'
+
+env GIT_COMMITTER_DATE 2024-01-30T10:53:00+08:00
+env GIT_AUTHOR_DATE 2024-01-30T10:53:00+08:00
+exec git add extra.go
+exec git commit -m 'add extra.go'
+
+# Assume the tree object from initial commit is not available (e.g. partial clone)
+exec git log --pretty=%T
+cmp stdout $WORK/.git-trees
+
+rm .git/objects/66/400c89b45cc96da36d232844dbf9ea5daa6bcf
+
+# Build the module, which should succeed
+go build -v -buildvcs=true
+
+-- $WORK/repo/go.mod --
+module github.com/golang/issue65339
+
+go 1.20
+-- $WORK/repo/main.go --
+package main
+
+func main() {
+	println("hello, world")
+}
+-- $WORK/repo/extra.go --
+package main
+-- $WORK/.git-trees --
+ac724c6e5e3f86815e057ff58a639cab613abf28
+66400c89b45cc96da36d232844dbf9ea5daa6bcf