My first thought was that filtering either for posts that have been marked as solved, or posts that have been liked by a staff member would work. Unfortunately, neither of those actions trigger a webhook. I think there are good reasons for not triggering a webhook on likes, but possibly something could be developed to trigger a webhook when a topic is marked as solved.
For triggering webhooks on specific posts with the current Discourse functionality, you could try setting up a webhook that fires on Flag Events. On Zapier you could filter the flagged posts by looking for posts that have been flagged as “Something Else” by a specific user on your site.
The easiest way to see the payload that gets passed with a Flag Event is to create a webhook on Discourse with the Flag Event selected as its trigger. For testing this, you can enter any URL into the webhook’s Payload URL field, for example http://example.com. After flagging a post on your site, go to Admin / API / Webhooks and click on the ‘Delivery Status’ link to get to the webhook’s request list.
Click on the Request button to see the payload that has been passed by the webhook.
On Zapier you should be able to access any of the values in the request’s Payload. To filter for posts that have been flagged as “Something Else” by a specific user, you’ll need to check that the request’s flag_type is notify_moderators and that the request’s created_by field is set to the username of the user you would like to trigger your Zapier action.