https://github.com/Azure/WALinuxAgent - I think this is the equivalence of GCP guest-agent, serving similar functionalities, and is pre-installed on all official images, otherwise basic things like authentication and image baking will break.
By setting the provisionVMAgent property to false when creating a virtual machine, WALinuxAgent should run with all extensions disabled, and I think that's as minimal as a Linux VM can go on Azure.
This property, however, can't be set via https://github.com/ansible-collections/azure, which is of course another lovely OSS project by Microsoft. I didn't bother to send a PR.
The OMI agent seems to be a different beast that is way more obnoxious. The closest thing on GCP is probably the collectd agent and the fluentd agent installed for Stackdriver Monitoring and Stackdriver Logging? Plus whatever OS config to enable unattended upgrades.
I just learnt from this HN thread about the SSM agent on AWS. That one does seem equally obnoxious as the OMI agent.
I have to say the problem is not oss, not agents, but Microsoft.