I have a flow I've been working on that deploys a SharePoint site, and creates a few lists based on custom content types in the global content type hub.
I have the following steps to create a list and apply a content type:

After some experimenting, I have confirmed that the above works, but only with the default content types. i.e. "0x0103" is fine, but my custom "0x0100AC4AE1EDCA551B478B245F71BB69####" content ID does not work, it's a BadGateway or Unauthorized error.
I've determined that the content type hub is not auto-publishing to newly created sites. If I send an http request to add one of my new content types to the list, I cannot. But, if I manually add the content type to a list, then remove it from the list and re-attempt the http request, it works. Thus, I've concluded I need to pull in the global content type gallery somehow.
I found this article about the new content type publishing What’s changed in content type publishing - Microsoft Support
contentType: addCopyFromContentTypeHub - Microsoft Graph v1.0 | Microsoft Learn
I've set up the http request and attempted the following URIs, but I'm getting invalid endpoint errors. Does anyone know what I'm doing wrong on this request?
_api/site/contentTypes/addCopyFromContentTypeHub
_api/web/contentTypes/addCopyFromContentTypeHub
/contentTypes/addCopyFromContentTypeHub
/contentTypes/addContentTypesFromHub
Method inspired by sharepointcass Create a SharePoint list, add/remove content types and updating the default SharePoint list view through REST API in Power Automate – SharePointCass