I couldn't find a way to do it only using the Azure DevOps API, because Wiki attachments can be created but not deleted, as no respective call exists. Also, using Attachments - Create files can not be overwritten, whereby unique naming and wiki page upates would have to be implemented.

The solution I implemented now is based on Wikis in Azure being repositories as well. In the runner, after I updated images, I clone the wiki repo using git, replace files in the .attachements folder, create a commit and push it.