datuwu

But I'm not sure that problem solved for people facing similar situation.

My problem is solved, it appears on my Java version already. Thanks a lot.

Update: 

I also followed this website's instructions:
 https://help.minecraft.net/hc/en-us/articles/26560321236621
 then visit this page:
 https://www.minecraft.net/en-us/msaprofile/mygames/editskin

 I scrolled down and didn't see a "15th Anniversary Cape" that existed.  Similar to Minecraft Launcher.  (b.2.24.27-1.7.2)

Update: It's been about 12 hours since I bought Minecraft and collected the cape, it still doesn't appear on the Java version to use.