I still don't have the cape on bedrock as of 14 september
Yes, but is says that once you have the cape it should show up on both accounts immediately. According to the article from minecraft.net: "We will begin rolling out the vanilla cape to eligible players on Wednesday, August 31st. However, it can take up to two weeks for the cape to appear in your account. Once it arrives, the cape should show up in your Dressing Room and Skin Customization menus automatically in both versions of the game. "
In my case the cape has arrived, but the cape is only visible in the java launcher.
I have the same issue. But I have seen instances where people actually got the cape on bedrock.
This is no longer an issue in the latest update
I just received my cape on bedrock. thanks a lot.