Hello, good day and thanks for your question. Sorry to know about this issue that you have encountered with your Minecraft cape.
If you are unable to access Bedrock (like the alternative methods for Linux - e.g BedrockOnLinux) or if there is no alternative way from your end to do it, please take note that there might be delays specifically when there are other players worldwide which is doing the same thing and if it still has not arrived then you can also reach out to the Minecraft team at https://aka.ms/Minecraft-Support/ for your account to be checked as well.