‘Pilot-in-command under supervision’ (PICUS) means a co-pilot performing, under the supervision of the pilot-in-command, the duties and functions of a pilot-in-command.
.... and if you check the definition of co-pilot you will find that it (and, therefore, PICUS) relates only to multi-pilot aircraft. The fact is that, in the UK at least, the terms in FCL.010 mean precisely what the CAA chooses them to mean - just like the rest of the Regulation.