Hi @Vasek Polak
You can perform using dump and restore method.
You can use pg_dump to extract a PostgreSQL database into a script file and psql to import the data into the target database from that file. If you want to migrate all the databases, you can use pg_dumpall to dump all the databases into one script file.
Here is an articles- https://learn.microsoft.com/en-us/azure/postgresql/migrate/how-to-migrate-using-dump-and-restore
https://learn.microsoft.com/en-us/azure/postgresql/flexible-server/how-to-pgdump-restore
Thank you!