I just feel this is a very complex and convoluted story... and usually, my gut feeling is they are difficult to believe.

My feeling is you wanted to go and have your dream holidays in the Maldives, so booked the flights. But then you realised that actually Maldives is expensive and not necessarily good value. So you thought Thailand would be the perfect alternative for your dream holidays.

Then you realised you could use the "complications, cut offs, log in fails, errors,.." as a complaint and try to convince IbPlus to rebook you into your BA flight. Apparently they "agreed to it". I feel this was more like "we can make you another reservation, but you would need to pay for it". So they did the reservation, but isnīt it suspicious that they make the reservations without asking you anything, a credit card number or whatever? This is a BIG RED FLAG (I have a similar story, once I wanted to redeem Flying Blue miles for a Air Bangkok flight - phone agent could make the reservation, but not price it. They told me back office would call me back to take payment. Obviously they never did, but I had to chase them. Eventually, I got to a competent agent that ticketed the reservation).

And now 4 or 3 days before your planned dream holidays departure, you realise your BA booking was actually not completed. IMO, not surprising at all.

Then you say you called BA (I do not know why) and they transferred you to Iberia??? Tbh this must be a first. Usually they say "you need to contact Iberia (Plus)".

My advice, get some cash tickets to Thailand in economy (leaving tomorrow, +420GBP - if you leave on Monday even cheaper). And deal with the taxes and fees of your Qatar Airways redemption once you are back.