Welcome to Shopify Community. My name is Olivia and I work here.
Thanks for sharing your question. Let's take a look at some of our most popular email marketing apps I shortlisted for you below:
While it is best to check with each app's dev for any specific functionality you need, I did find these top contenders mention embedding forms or survey templates while researching for you. Of the three I shared, Klaviyo specifically stands out to me with their explicit instructions on how to embed a survey into an email campaign.
I also found this related forum post I encourage you to check out written by one of my colleagues. I trust you might be interested in further reading that post to learn about some of your other options, including some survey apps from our App Store.
Please let me know what you think, and if there's any other specific functionality you are looking for in your survey or email newsletters.
I look forward to your reply,