Why doesn't Oracle expdp create the dump file?
It was an issue with the TEMP tablespace, which was stored in a disk partition with no more available space.

Following CaM's suggestion (thanks!), I checked that my_user doesn't have the EXP_FULL_DATABASE role, so I launched again the expdp command but without the schemas parameter. For some reason, doing it this way Oracle finally took pity of me, gave up its shenanigans and decided to show the error:

ORA-39125: Worker unexpected fatal error in KUPW$WORKER.DISPATCH_WORK_ITEMS while calling
           DBMS_LOB.CREATETEMPORARY []
ORA-01652: unable to extend temp segment by 128 in tablespace TEMP


After "moving" the temp datafile to another partition and having a nice fight with Unix to release the disk space, the expdp finally works again.