I don't understand either.

Not sure what you mean by "my colleague received a refund confirmation for a hold flight". From your timeline, that cancelled no-name booking is not part of the picture. Your colleague then did a new booking for LHR-SIN before 11:35am (time of the call to BA).
Apparently, but details are scarce, you colleague was under pressure and mistakenly put the name of "P" rather than "D" in the new LHR-SIN booking. I am afraid that the confusion created by multiple windows comes from your colleague, not BA IT system.

That error in name could have been corrected within 24 hours (I guess by Friday morning), but it was not. Whether you found the BA supervisor impolite on Monday is beyond the point; this was well after the cooling period for name change had expired.

Your major complain ("original issue") is that your colleague called BA thursday morning to check that the flight on hold had truly been canceled. And clearly it was. Then she was told that there were no other booking un the credit card number. I am a bit surprised that the phone agent could access all bookings done under a credit card number (especially as the ticket had not been issued yet). Maybe your colleague gave "D" name and the agent found no booking under his name as the booking was done under "P". If the new booking had been done before the call, she could have simply given the booking reference to inquire about the status.

It is sad that your colleague did not check the ticketing emails that arrived five hours later, but I find it hard to fault BA.