Let Operation handler classes specify a finish method to run on the completion of a bulk operation

Mostly look good to me, do you want to provide an explanation of what you've done and what API changes it involves to help verify what you've written does what you want?

Also, I would imagine passing through the $success variable into ViewsBulkOperationsBaseOperation::finish() would be helpful so that the finish function can take status into consideration.

public function execute($data, array $context, &$vbo_sandbox) {
  ...
}

As we have type hinting for $context, it would make sense to have it for $vbo_sandbox as well for consistency.

/*
 * @param $vbo_sandbox
 *   An array of variables to persist between the batch calls.
 */

Is it worth mentioning that it also gets passed to the finish() method, as that may well be the more common usage and is certainly yours...

Shouldn't there also be a change to allow hook_action_info() to define the finish function?

I consider it bad DX to have to override the operation plugin every time I want to execute some code after a set of entities.
Let's make it a callback defined by hook_action_info() like #5 suggests.

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Here is the patch re-rolled... I've not addressed the issue raised in #5. However, I'm not sure I agree with it, as this is allowing the operations themselves to do things. I wonder if that is really a separate issue that may be best solved with a rules event or similar?