Id::Invalid -> Id::None (#4834)

High level, replacing `Id::Invalid` with `Id::None` and `Id::is_valid`
with `Id::has_value` for clarity, as discussed
[here](https://discord.com/channels/655572317891461132/655578254970716160/1331664574545395794).
The `IntId` refactoring is needed together with `AnyIdBase` because it's
also used with `ValueStore`.

Note, trying to be careful not to rewrite `EnumBase::InvalidIndex`, or
`is_valid` in general (e.g., `IdKind::is_valid`).

I've tried to sequence commits here:

1. Automatic replacements:

- `((?:Id|Index)(?: |::|\(|Base(?:\(|::)))Invalid((?:Index)?\W)` ->
`$1None$2`
  - `<invalid>` -> `<none>`
  - `InvalidNodeId` -> `NoneNodeId`
  - `/\*invalid\*/` -> `/*none*/`
  - `id((?:_|\(\))(?:\.|->))is_valid` -> `id$1has_value`

2. Manual edits:

  - In `int.h` and `int_test.cpp`
    - `IntT` has `is_value`, which I'm renaming to `is_embedded_value`.
    - Manual edits to comments in this file.
  - `AnyIdBase` and `IdBase`
- Declaration of `is_valid` -> `has_value`, `InvalidIndex` ->
`NoneIndex`.
  - In `ids.h` and `ids.cpp`
    - `is_valid` -> `has_value`
- `// An explicitly invalid ID.` -> `// An ID with no value.`; similar
for index
    - Various math on `InvalidIndex` -> `NoneIndex`
    - Various mentions of "valid" in comments
  - In `value_store.h`, for `IdT::Invalid`, plus one comment
- In `impl.h` and `tokenized_buffer.h`, we had different initialization
of `::None` values (versus `ids.h` syntax) that I fixed manually.
  - Spot checks to compile
- Particularly where `is_valid` replacements didn't catch spots due to
different naming.

3. Autoupdate tests

4. verbose.carbon (NOAUTOUPDATE)

5. Comment spot checks

Note there are probably other mentions of "Invalid" that should be swept
up, but I'd like to argue for merging and separating out remaining
cleanup since this is so sweeping (and likely to hit merge conflicts
from churn). We'll probably have lingering mentions of "invalid" for a
bit regardless, just because there are uses of "invalid" in non-Id APIs.

toolchain/sem_ir/builtin_function_kind.cpp

@@ -31,7 +31,7 @@ constexpr int MaxTypeParams = 2;
 struct ValidateState {
   // The type values of type parameters in the builtin signature. Invalid if
   // either no value has been deduced yet or the parameter is not used.
-  TypeId type_params[MaxTypeParams] = {TypeId::Invalid, TypeId::Invalid};
+  TypeId type_params[MaxTypeParams] = {TypeId::None, TypeId::None};
 };
 
 // Constraint that a type is generic type parameter `I` of the builtin,
@@ -42,7 +42,7 @@ struct TypeParam {
 
   static auto Check(const File& sem_ir, ValidateState& state, TypeId type_id)
       -> bool {
-    if (state.type_params[I].is_valid() && type_id != state.type_params[I]) {
+    if (state.type_params[I].has_value() && type_id != state.type_params[I]) {
       return false;
     }
     if (!TypeConstraint::Check(sem_ir, state, type_id)) {
@@ -112,7 +112,7 @@ struct AnyFloat {
 // Checks that the specified type matches the given type constraint.
 template <typename TypeConstraint>
 auto Check(const File& sem_ir, ValidateState& state, TypeId type_id) -> bool {
-  while (type_id.is_valid()) {
+  while (type_id.has_value()) {
     // Allow a type that satisfies the constraint.
     if (TypeConstraint::Check(sem_ir, state, type_id)) {
       return true;