This will allow you to achieve an embedded YouTube video with vue-dompurify-html
<template>
<div>
<div v-dompurify-html="test"></div>
</div>
</template>
<script>
import Vue from 'vue'
import VueDOMPurifyHTML from 'vue-dompurify-html'
Vue.use(VueDOMPurifyHTML, {
default: {
ADD_TAGS: ['iframe'], // this one whitelists Youtube
},
})
/* eslint-disable no-useless-escape */
/* eslint-disable prettier/prettier */
export default {
data() {
return {
test: '<iframe class=\"ql-video\" frameborder=\"0\" allowfullscreen=\"true\" src=\"\https://www.youtube.com/embed/9_MzJ9QkiHU\"></iframe><p><br></p><p><br></p><p>Description</p>'
}
}
}
</script>

In case you want to go from
'<iframe class=\"ql-video\" frameborder=\"0\" allowfullscreen=\"true\" src=\"\https://www.youtube.com/embed/9_MzJ9QkiHU\"></iframe><p><br></p><p><br></p><p>Description</p>'
into something more clean (for Vue) like this
"<iframe class='ql-video' frameborder='0' allowfullscreen='true' src='https://www.youtube.com/embed/9_MzJ9QkiHU'></iframe><p><br></p><p><br></p><p>Description</p>"
you can use this method
string.replaceAll('"', "'")
The answer to this was found from this commit: https://github.com/eternagame/eternagame.org/commit/dfcfb6bf8fc77495bb17ea9231091ca5d4f2cbad#diff-841254fe75488c1bd4cd7f68f00b4be0e48dcfbc4a16b45847b68295e0e3b27bL13-R25
Description
", In database description is stored like this – chaitanya gupta May 28 '21 at 14:10