Fix: captcha transition multi children issue

• Resolve #2751 (closed)
• Refactor captcha_button.vue file for cleaner code.
• Fix typo verfiedTanuki to verifiedTanuki

This has been a long existing issue in this file, this MR will fix that issue and also resolves #2751 (closed) for the upcoming migration to Vue3.

Since this fix is also acceptable by the main-jh branch, there was no need to target to the migration feature branch.

CleanShot_2023-04-26_at_11.46.17