Rename Parse::State to Parse::StateKind (#5249)

Also renames variables of that type to match. A follow-up PR will rename
`Parse::StateStackEntry` to `Parse::State`. This is more consistent with
the naming of similar enums elsewhere in the toolchain, and with the
prevailing practice of using `state` rather than e.g. `entry` as the
name of a `StateStackEntry`.

See also discussion
[here](https://discord.com/channels/655572317891461132/963846118964350976/1326280585592700990)

toolchain/parse/parse.cpp

@@ -28,12 +28,12 @@ auto Parse(Lex::TokenizedBuffer& tokens, Diagnostics::Consumer& consumer,
   context.AddLeafNode(NodeKind::FileStart,
                       context.ConsumeChecked(Lex::TokenKind::FileStart));
 
-  context.PushState(State::DeclScopeLoop);
+  context.PushState(StateKind::DeclScopeLoop);
 
   while (!context.state_stack().empty()) {
-    switch (context.state_stack().back().state) {
+    switch (context.state_stack().back().kind) {
 #define CARBON_PARSE_STATE(Name) \
-  case State::Name:              \
+  case StateKind::Name:          \
     Handle##Name(context);       \
     break;
 #include "toolchain/parse/state.def"