After hours of searching and refusing to edit the pipeline in the portal for what is meant to be automated configuration, it looks to be a permissions issue.
In my config, I have a pipeline used for the automate building of the environment (and subsequent pipelines) running in the context of the 'Project Build Service' account.
When running the script used in the pipeline for config locally, in the context of my user account, it creates the pipeline without issues and attaches the Default agent pool for YAML as 'Azure Pipelines' (As wanted). However, running the same script in the context of the 'Project Build Service' account, it does not apply this setting. Therefore, it's a permissions issue that annoyingly gives you a silent error instead of failing.
To fix:
Navigate to 'Project Settings > Agent Pools > Azure Pipelines (Your pool) > Security'
Under 'User permissions', click 'Add'
Select the account your automated process is running in the context of. In my case, this is the Project Build Service account.
Assign them role of 'User'.