This would enable microsoft/TypeScript#14423.
I am mostly describing changes to protocol.ts in the TypeScript repository here.
@mjbvz @egamma @mhegazy we discussed this today.

1

The returned CodeAction in a code action request may include a list of commands.

export interface CodeAction {
    description: string;
    changes: FileCodeEdits[];
    command?: {};
}

A code action may even have an empty changes list and consist of only a command.
We could choose specify that command must an of commands, although I'm not sure if that's worth bothering with.

2

If the code action is accepted, the editor must send the commands back to the language service to actually be carried out. This means needing a new request type, "applyCodeFixCommand". This looks like:

export interface ApplyCodeFixCommandRequest extends Request {
    command: CommandTypes.ApplyCodeFixCommand;
    arguments: ApplyCodeFixCommandRequestArgs;
}

export interface ApplyCodeFixCommandRequestArgs extends FileRequestArgs {
    command: {};
}

The contents of command will just be what was sent to the editor.
(Typically this will include a "type" field so the language service can dispatch on the type of action.)

3

The language service should send a response when the action is complete.

export interface ApplyCodeFixCommandResponse extends Response {
    body: {};
}

I'm thinking we can just reuse the message field for error reporting and for a successful response. (Currently the field is documented to only be used if success is false.) We could put that in the body, but then it seems redundant.