I voted during the last year mob vote and I was given the Cherry Blossom cape on Java Edition, but didn't get it on the Bedrock Edition

Me too, but it doesn't seem to me that capes migration doesn't work from java to bedrock.

The requirements for this cape were different. The Bedrock cape required you to join the event server. Voting was not a requirement.

The requirements for this cape were different. The Bedrock cape required you to join the event server. Voting was not a requirement.

If the requirement for getting the cape on Bedrock was joining the event server then why people who joined it got capes on both versions on Minecraft instead of only for Bedrock?

Because the requirement for the Java cape was voting. People who got the cape in both editions joined the event server and voted.

Because the requirement for the Java cape was voting. People who got the cape in both editions joined the event server and voted.