The error you are seeing is triggered because this relation file exceeds MAX_TAR_MEMBER_FILELEN or 8GB for a single tar member, which is as well the norm for tar.
I thought PostgreSQL would break the file if it grows beyond 1GB (1GB is segment size which one can modify while compiling). Am I missing something or have I got it totally wrong?
> Is there a solution/workaround? Not use a pg_basebackup but an external backup solution or a custom script. Break this relation file into several pieces by doing some partitions on it.
> Can I break up the referenced file somehow?
Partitions on the parent table.
Which might have other implications on the performance if the queries do not use Partition key in where clause.