Hi @MWarn,
The size of the disk varies by SKU, e.g. the temporary storage for a Y1 (Consumption) is only 500MB. More than likely, the temporary storage has gotten full. You may be able to use the Kudu console to remove any items. However, it's important to note that the main site and scm site doesn't share the same temporary storage. There is a legacy app setting, WEBSITE_DISABLE_SCM_SEPARATION
, that force both sites to use the same storage but it's use isn't recommended.
I think the best two options is to either use a slot setting or app service plan scaling. You can create a test slot, do the deployment, test, then swap the slots. You can then either decide to keep the slot or delete it. The other option is to scale up your app service plan to EP1, deploy, then scale back down.