Syntex is not pushing content type to Hub site and associated sites

I am trying to create content type in content type hub and publish it toa hub site and siate associated to it. There are 3 different content types

1. Custom content type from Document Content type
2.  Custom content type from Site Page
3. Custom content type from List item

Issue is all above content types are not getting pushed to Hub site and site associated to hub sites. It only worked for a custom content type created from Document content type, only for a new site joining hub after content type was published. Its been 24 hrs but I do not see this custom document content type pushed to other sites in hub. Also it is not getting pushed to Default Document and Site Page libraries.

My tenant has Syntex licenses and I see option to select and push to hub sites. I have followed https://learn.microsoft.com/en-us/microsoft-365/syntex/push-content-type-to-hub 

Questions:

1. Does it support site page and list based content types?
2. Does is push content types to existing default library , Site Pages, Documents etc.
3. How many level of hub association it supports? I have nested Hub site architecture