How to automate deployment using gitlab CI/CD with HA Supervised

I am looking to automate the deployment of my configuration with Gitlab pipelines.
I already implemented the preflight phase (yamllint, config check etc) and the test phase (against current and dev versions), following Frenck’s gitlab-ci.yaml. So far so good.

I am now trying to add a deployment phase so that every commit that passes the testing phases is pulled on the production server and ha is restarted automatically. I found a few resources (mainly here and here) that suggest methods to achieve this.
However, these method do not fit me, because they rely on SSH for deployment (and a docker image), while I do not want to expose the SSH port (and I use HA Supervised). My install has a publicly accessible address though (something like homeassistant.example.com).

In his blogpost, @robconnolly says:

Similar to the approach above you could trigger the HASS webhook handler from a job in your Gitlab runner directly with CURL (rather than using the built in webhooks). This has the advantage over the previous two approaches that it gives you an explicit deploy stage in your pipeline. This is turn gives you the ability to track deployments via environments. It’s also potentially a lot simpler, since it would only be triggered if the previous stages in the pipeline passed. You also wouldn’t have to parse the JSON payload.

This looks like the perfect solution for me. I searched for quite some time, but I still can’t find any doc detailing this approach a bit more. Could someone guide me in the right direction?

OF COURSE, 5 minutes after posting this, I come across a blogpost that explains it all.

TL;DR; Use a webhook trigger, that launches an automation to activate the git pull addon and then restart ha.