Are mutation methods required to be on the top level?

It’s possible but generally not a good idea because:

It breaks the spec. From section 6.3.1:

Because the resolution of fields other than top‐level mutation fields must always be side effect‐free and idempotent, the execution order must not affect the result, and hence the server has the freedom to execute the field entries in whatever order it deems optimal.

In other words, only fields on the mutation root type should have side effects like CRUD operations.

Having the mutations at the root makes sense conceptually. Whatever action you’re doing (liking a post, verifying an email, submitting an order, etc.) doesn’t rely on GraphQL having to resolve additional fields before the action is taken. This is unlike when you’re actually querying data. For example, to get comments on a post, we may have to resolve a user field, then a posts field and then finally the comments field for each post. At each “level”, the field’s contents are dependent on the value the parent field resolved to. This normally is not the case with mutations.

Under the hood, mutations are resolved sequentially. This is contrary to normal field resolution which happens in parallel. That means, for example, the firstName and lastName of a User type are resolved at the same time. However, if your operation type is mutation, the root fields will all be resolved one at a time. So in a query like this:

mutation SomeOperationName {
  createUser
  editUser
  deleteUser
}

Each mutation will happen one at a time, in the order that they appear in the document. However, this only works for the root and only when the operation is a mutation, so these three fields will resolve in parallel:

mutation SomeOperationName {
  user {
    create
    edit
    delete
  }
}

If you still want to do it, despite the above, this is how you do it when using makeExecutableSchema, which is what Apollo uses under the hood:

const resolvers = {
  Mutation: {
    post: () => ({}), // return an empty object,
  },
  PostMutation: {
    edit: () => editPost(),
  },
  // Other types here
}

Your schema defined PostMutation as an object type, so GraphQL is expecting that field to return an object. If you omit the resolver for post, it will return null, which means none of the resolvers for the returning type (PostMutation) will be fired. That also means, we can also write:

mutation {
  post
}

which does nothing but is still a valid query. Which is yet another reason to avoid this sort of schema structure.