Our team has been discussing how we can utilize the feedback widget to better understand metrics on our users and applications. This also includes the desire to include custom fields in the feedback to track application specific things. If we could add custom fields into feedback, we could let the feedback tool provide that data our users may not be able, such as object IDs or application states.
Still, you can achieve that with current feedback. For sure, it's not perfect, but it's possible.
You can use your custom dialog for collecting feedback with the fields that you expected to be filled, and map them to a JSON and send the JSON as the content of the feedback.
Later, you can export this data from the app Insights and use an Excel to view your custom fields.