First edited profile can overwrite second edited profile in Dressing Room

From the beginning of 1.21.30, the dressing room UI causes a bug, while you editing your preferred skins, and then edit another skins, it displays your previous skins, and it look very terrible.

There are 2 methods to reproduce this issue:

Method 1: from the video provided by the reporter:

1. With Minecraft open, go to Dressing Room
2. Have 2 classic skins prepared, the skins have to be different so the result would be more obvious
3. Try editing the first skin, this unequipped the cape if there's one, so a re-equip of a cape is required, otherwise it stays unequipped. (what the reporter faced in this step was MCPE-179630)
4. Return to Dressing Room
5. Try editing the second skin

Expected result: The second skin loads without any problem.
Actual result: The second skin loads, but gets replaced with the first one after some time.

Method 2: simplified to the main point only:

1. With Minecraft open, go to Dressing Room
2. Create / edit the first character / skin
3. Return to Dressing Room
4. Create the second character / skin if there is a free slot, if not, try editing another slot that's not the the first one

Expected result: the second character / skin loads as their own.
Actual result: the first character / skin loads when you try to edit the second character / skin, and can overwrite the second character / skin / capes with the first one.

Workaround to both methods: Restart Minecraft if you want to edit the second character / equip another skin for the second one.