Hello sanjay .s,
Note that cape/skin sync issues are handled by Mojang's help team. So, for future assistance, you should reach their Minecraft Support first.
That said — this is actually expected behavior. Promotional capes redeemed on the Minecraft site show up in Bedrock's Dressing Room first, and to make them appear in Java you have to manually select the cape in the Java skin editor.
Reference: Activate Promotional Capes and Character Creator Items on Your Minecraft: Java Edition Profile
- Open Minecraft: Bedrock Edition and go to the Dressing Room — confirm the Home Cape is there
- Exit Bedrock, then open Minecraft: Java Edition
- Go to Skins > highlight your current skin
- Select … > Edit > pick the Home Cape > Save & Use
- Close and restart Java Edition
After restart it should render in-game. If it doesn't show up immediately after redemption, there can be a short sync delay (community reports up to ~24h) before the cape becomes selectable in Java's editor.
If it's still missing after that, Minecraft Support at https://help.minecraft.net is the right next stop.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.
Please note that our forum is a public platform, and we will modify your question to hide your personal information in the description. Kindly ensure that you hide any personal or organizational information the next time you post an error or other details to protect personal data.