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/testdata/function/declaration/fail_missing_name.carbon

@@ -0,0 +1,17 @@
+// 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
+//
+// AUTOUPDATE
+
+// CHECK:STDERR: fail_missing_name.carbon:[[@LINE+3]]:4: `fn` introducer should be followed by a name.
+// CHECK:STDERR: fn ();
+// CHECK:STDERR:    ^
+fn ();
+
+// CHECK:STDOUT: [
+// CHECK:STDOUT:   {kind: 'FunctionIntroducer', text: 'fn'},
+// CHECK:STDOUT:   {kind: 'InvalidParse', text: '('},
+// CHECK:STDOUT: {kind: 'FunctionDeclaration', text: ';', has_error: yes, subtree_size: 3},
+// CHECK:STDOUT: {kind: 'FileEnd', text: ''},
+// CHECK:STDOUT: ]