use this code:

<div id="vueapp">
  <textarea v-model="jsonstr" rows="8" cols="40"></textarea>
  <pre>{{ jsonstr | pretty }}</pre>
</div>

and JS:

new Vue({
  el: '#vueapp',
  data: {
    jsonstr: '{"id":1,"name":"A green door","price":12.50,"tags":["home","green"]}'
  },
  filters: {
    pretty: function(value) {
      return JSON.stringify(JSON.parse(value), null, 2);
    }
  }
})

You can add a filter to stringify the data in a nicer format.

filters: {
  pretty: (val, indent = 2) => {
    if (typeof val !== "object") {
      try {
        val = JSON.parse(val)
      } catch (err) {
        console.warn("value is not JSON")
        return val
      }
     
      return JSON.stringify(val, null, indent)
    }
  }
}

Use CSS white-space or simply use a <pre> tag to keep formatting in your template

<pre>{{ entrie.response.content.text | pretty(4) }}</pre>

Demo ~ https://jsfiddle.net/ktz49q1h/

Note that filters are not supported in Vue3. See the migration strategy for solutions.