Hi @MS Techie , welcome to Microsoft Q&A forum.
Certificate authentication is still not supported on 'Flexible Server(Preview)' same as 'Single Server'. I enquired the same with internal product team and as latest as the last week updates it is still not supported. (Link for older issue). As mentioned by you, we currently have Active directory authentication for PostgreSQL. However, I will be in touch with internal team and will update the forum anytime this feature is on roadmap.
For pricing details, please refer to below link:
https://azure.microsoft.com/en-au/pricing/details/postgresql/flexible-server/
Also before choosing the appropriate server, I would recommend to go through the link below as it has details available at features level:
https://learn.microsoft.com/en-us/azure/postgresql/overview-postgres-choose-server-options
Please let us know if any other other details needed, and we would be delighted to discuss further.