After much investigation, I'm still none the wiser to what caused this issue however I have now resolved it. I'm not sure if this is helpful for anyone but I spent many hours creating new connections to try and sort it out.
Steps I took to fix this was:
-Create a new sql server and database and make sure they're in the same resource group.
-Rather than creating a 'Insert new row' element in azure, I instead created a 'Execute a SQL query V2'. I connected using a the sql server authentication and made sure I could query my database first so that I knew my details were correct. Once the connection was setup, I then was able to see my server, database and table from the drop downs without manually typing them in (this is key or else it will not work).
-I then deleted this and created 'insert a new row' which I originally had using the connection that I had just created. Then select again the credentials from the drop down.
I think in the end there might have been a caching issue where it just took some time for the fields to appear in the drop down.
Feel free to also share if you've ever encountered anything like before and what steps you took to resolve it.