Welcome to the Community! Definitely a great place to gather some input regarding anything about the platform!
With regards to your inquiry, as you can see, we have some great contributors like @KetanKumar and @PageFly-Victor that have provided some apps for you to look at already. Both apps are great and will allow for you to send out those notifications that you are after.
Definitely give those two apps a review to see how they work to what you are looking for then we can go from there. If the apps do not work, please let us know why so we can sift through more apps from the Shopify App Store to see what other options may work for you.
Also, if you are finding that your need is too specific for an app to accomplish, you can also consider hiring a Shopify Expert as an alternative. These are trusted freelancers who are well-versed on the platform.
I’m not sure if that form in your footer is creating new customers in your shop with the proper “subscribed” status (this status is stored in Shopify along the email and rest of the customer information). If it is, there’s an automation for new subscribers built-in Shopify itself (Marketing > Automations), you may want to have a look at that, emails are sent with the Shopify Email app: