I Also do Do not Have it as of 9/10/2022.
Yes they said that you would not get the capes immediately on august 31 but they did say when you get the cape you get it on both platforms at the SAME TIME.
I am having the same issue. i got it on the java edition launcher but not in the bedrock edition wardrobe.
[media][media]I am also having this issue on Windows 10 ever since the added the hotfix yesterday. I can't download the cape, even though I owned it prior. I am going to wait for them to fix it as installing beta is too much hassle.
Ok seriously Mojang we have been waiting for 2 weeks now and this bug still exists. Is it that hard to just fix the bug. and give us our capes?