[build] Remove references to //zircon/public/lib/FOO

These targets are now just redirection groups to libraries
under //zircon/system/ulib/, so replace these references with
their destination instead.

Bug: 70426
Change-Id: Id60757d906625d8d5a56b2f050c08306b4c146a6
Reviewed-on: https://fuchsia-review.googlesource.com/c/third_party/leveldb/+/487357
Fuchsia-Auto-Submit: David Turner <digit@google.com>
Reviewed-by: Shai Barack <shayba@google.com>
Commit-Queue: Auto-Submit <auto-submit@fuchsia-infra.iam.gserviceaccount.com>
diff --git a/BUILD.gn b/BUILD.gn
index f767d6d..9200f40 100644
--- a/BUILD.gn
+++ b/BUILD.gn
@@ -130,16 +130,16 @@
 
   public_deps = [
     "//sdk/fidl/fuchsia.io",
-    "//sdk//lib/fdio",
+    "//sdk/lib/fdio",
     "//third_party/re2",
     "//third_party/snappy",
-    "//zircon/public/lib/async",
-    "//zircon/public/lib/async-cpp",
-    "//zircon/public/lib/fit",
-    "//zircon/public/lib/zx",
+    "//zircon/system/ulib/async",
+    "//zircon/system/ulib/async:async-cpp",
     "//zircon/system/ulib/async-loop:async-loop-cpp",
     "//zircon/system/ulib/async-loop:async-loop-default",
+    "//zircon/system/ulib/fit",
     "//zircon/system/ulib/syslog",
+    "//zircon/system/ulib/zx",
   ]
 
   public_configs = [ ":leveldb_config" ]