Create proper reindex/push settings responses for AJAX based events.

[tw2113]

In both re_index() and push_settings() methods from Algolia_Admin class, we return wp_send_json() responses for successful try/catch instances. However, if we do end up in the catch portion, we just do echo esc_html( $exception->getMessage() ) and then throw the exception up the chain.

While I'm not presently sure about throwing the exception further, we should probably amend the sections to do:

wp_send_json(
    [
        'responseText' => $exception->getMessage()
    ]
);

that way the alert gets the proper values to show.

[tw2113]

PR for this #457

[tw2113]

Tentatively marking this as 2.9.0 with some help on a forum support ticket testing, but this would be the first to be punted to a later release for all of what's on the 2.9.0 milestone.

[tw2113]

Haven't had confirmed success with this changing alerts content, so bumping to a later release.

[tw2113]

Based on some related yet not testing, having throws in this spot may trigger enough info from the exceptions, in the admin notices already. However, we have other spots that are not bubbling the thrown exceptions, and just attempting to log via error_log() that could potentially use some enhancement here.

[tw2113]

Correction, plucking from #506, which has been tested/confirmed.