Refactor checking flow to allow for ordering based on import/package. (#3379)

As I was working on this, I noticed `import` and `library` syntax needs
to be fixed for how it imports the current package, and for `Main`
libraries. This mostly reflects the current state in its testing.

Otherwise, this should handle most of the errors I could think of:
dependency cycles, redundant imports, etc.

It does not actually deal with the nuances of cross-IR references.

---------

Co-authored-by: Richard Smith <richard@metafoo.co.uk>

toolchain/parse/context.h

@@ -300,6 +300,19 @@ class Context {
   auto RecoverFromDeclError(StateStackEntry state, NodeKind parse_node_kind,
                             bool skip_past_likely_end) -> void;
 
+  // Sets the package directive information. Called at most once.
+  auto set_packaging_directive(Tree::PackagingNames packaging_names,
+                               Tree::ApiOrImpl api_or_impl) -> void {
+    CARBON_CHECK(!tree_->packaging_directive_);
+    tree_->packaging_directive_ = {.names = packaging_names,
+                                   .api_or_impl = api_or_impl};
+  }
+
+  // Adds an import.
+  auto AddImport(Tree::PackagingNames package) -> void {
+    tree_->imports_.push_back(package);
+  }
+
   // Prints information for a stack dump.
   auto PrintForStackDump(llvm::raw_ostream& output) const -> void;