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Ways of Loading Data (PostgreSQL) to Synapse SQL Database
Using Data Factory
You can create the linked service to PostgreSQL on-premise using a data factory.

After you get the PostgreSQL, you will use COPY activity to move(copy) the data to blob storage. (SQL pool can create the table from the external table from the blob storage)
Using PolyBase
(1) Export the table to a flat file
Ref: Link
You can use any SQL developer tools, or command lines to export flat files from the relational database. For instance, you can use COPY command or pg_dump to export CSV files from the PostgreSQL tables.
(2) Upload the flat file to blob storage
There are many ways to upload files to the blob storage, but the most common ways to do are using az CLI or storage explore (provided by Microsoft)
Ref: Link
(3) Run Polybase process
Polybase is a technology that accesses external data stored in Azure blob storage, Hadoop or Azure data lake using T-SQL language. This is the most scalable and fastest way of loading data into an Azure Synapse SQL pool.