While browsing posts from the past on the On this day page, I saw the one about blog.gs from 2002.

Turns out the blog.gs ping mechanism is still working in exactly the same way after all these years (nowadays operated by Automattic).

As I don't run my blog with PHP anymore, I added the following step at the end of my deploy script.
It uses curl to peform the XML-RPC call of the weblogUpdates.extendedPing API with the parameters for my weblog.

curl -X POST -v ping.blo.gs -H 'content-type: text/xml' --data '<?xml version="1.0"?><methodCall><methodName>weblogUpdates.extendedPing</methodName><params><param><value>x-log</value></param><param><value>https://blog.x-way.org/</value></param><param><value></value></param><param><value>https://blog.x-way.org/rss.xml</value></param></params></methodCall>'