This could be enforced in the schema via triggers and/or security permissions. Cooperation from the client is not required.
EDIT: Oracle has append-only tables, and can also use "blockchain" to verify integrity. See the IMMUTABLE option on CREATE TABLE[0]. PostgreSQL doesn't appear to have append-only tables, so using security and/or triggers seems to be the only option there.
[0] https://docs.oracle.com/en/database/oracle/oracle-database/2...