Hi Rakshak Shrestha,
I understand that you are unable to migrate Postgres Single Server due to some issue stated.
I would like to inform you that, we have enabled the PostgreSQL single server for the next 30 days to migrate it to the Flexible Server, this is not extendable.
Use our migration service in Azure Database for PostgreSQL to simplify the migration experience. It provides both offline and online migration options. https://learn.microsoft.com/en-us/azure/postgresql/migrate/migration-service/tutorial-migration-service-single-to-flexible
Auto-migration option (offline mode only) can keep server name and DNS the same, so the application won’t need any connection string changes.
Note: Public Access needs to be enabled for the Single Server, and CMK server can’t be created using auto-migration.
I hope this information helps. Please do let us know if you have any further queries.