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/array/without_length.carbon

@@ -0,0 +1,19 @@
+// 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
+
+var x: [i32;];
+
+// CHECK:STDOUT: [
+// CHECK:STDOUT:   {kind: 'VariableIntroducer', text: 'var'},
+// CHECK:STDOUT:     {kind: 'Name', text: 'x'},
+// CHECK:STDOUT:         {kind: 'ArrayExpressionStart', text: '['},
+// CHECK:STDOUT:         {kind: 'Literal', text: 'i32'},
+// CHECK:STDOUT:       {kind: 'ArrayExpressionSemi', text: ';', subtree_size: 3},
+// CHECK:STDOUT:     {kind: 'ArrayExpression', text: ']', subtree_size: 4},
+// CHECK:STDOUT:   {kind: 'PatternBinding', text: ':', subtree_size: 6},
+// CHECK:STDOUT: {kind: 'VariableDeclaration', text: ';', subtree_size: 8},
+// CHECK:STDOUT: {kind: 'FileEnd', text: ''},
+// CHECK:STDOUT: ]