Numi

As a data point in case helpful to others; I applied on 3 April for the Avios Plus card, didn't receive an instant decision but was told I would be contacted within 5BDs. Obviously that didn't happen - no email, no letter, no call, nothing in my Barclays app - so I rang up today. Tried the number ending in 0900 which is a complete shambles with a ludicrous voice-management system and horrendous wait times, and then found that there is a dedicated number for Avios Plus 0800 161 5309 (in case that hasn't been posted before). Each time the call was answered in 5 mins. The first lady a spoke to was a bit useless, but I got someone really helpful when ringing up again after the first call got disconnected who chased this up and rang back when the second call got disconnected, too.

Apparently, my application was "referred for review" and there is no given time frame for when they will get back to me with a decision. But he did confirm they have it and someone is looking at it.
He did say that he considers this a bit rubbish, that the delay was likely exacerbated due to the holiday weekend, and that a new customer service system was implemented on Tuesday without telling the operators and so everyone is scrambling.

I do have a Barclays account and they were able to find my application that way, though I suspect that if I didn't, or if there had been a disconnect with my name, they wouldn't have been able to find it.

As others have said, I am extremely unimpressed by the entire process and will likely cancel the card - should I ever receive it - as soon as I get the bonus, should these issues persist.