Fix Custom Created Newsletter Signup Sections on Shopify Store

I need a Shopify expert to fix the newsletter signup sections embedded within my store please.

These were custom created quite a while ago but I'm just sorting me email marketing now!
So issue is that when someone enters their email in the sign-up box and presses the button, they are:
- not added to the list of subscribers
- a message does not appear to confirm they have successfully subscribed
The Shopify team tested another theme within my store and that worked fine (see screenshot added below, along with screenshots of the form sections in the back end of the website).
It is an issue within the theme, but turns out to be custom created.

I should like someone to fix this ideally whilst keeping the surrounding design the same (in terms of using brand fonts - where used - for the text around the sign-up forms). I've uploaded some screenshots of the 2 forms, from the following web page: https://duvethog.co.uk/

Thank you,

Phillippa