Rename parser dir to parse (#3178)

Continuing with #3070. Just a dir and file rename (mostly removing
prefixes, although for parse_tree_fuzzer and parse_tree_file_test I'm
dropping "tree" instead of "parse"). Everything in the parse dir should
be marked as a move.

toolchain/parse/handle_index_expression.cpp

@@ -0,0 +1,27 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+#include "toolchain/lexer/token_kind.h"
+#include "toolchain/parse/context.h"
+
+namespace Carbon::Parse {
+
+auto HandleIndexExpression(Context& context) -> void {
+  auto state = context.PopState();
+  state.state = State::IndexExpressionFinish;
+  context.PushState(state);
+  context.AddNode(NodeKind::IndexExpressionStart,
+                  context.ConsumeChecked(Lex::TokenKind::OpenSquareBracket),
+                  state.subtree_start, state.has_error);
+  context.PushState(State::Expression);
+}
+
+auto HandleIndexExpressionFinish(Context& context) -> void {
+  auto state = context.PopState();
+
+  context.ConsumeAndAddCloseSymbol(state.token, state,
+                                   NodeKind::IndexExpression);
+}
+
+}  // namespace Carbon::Parse