I then end up with a weird extra thin border underneath the textField.

It is listRowSeparator. you can make it hidden with this modifier:

.listRowSeparator(.hidden)

Also, the Form and the List have some default inset. You can customize them with this modifier:

.listRowInsets(EdgeInsets(top: 0, leading: 0, bottom: 0, trailing: 0))

It is important to put wich modifier where. There are other detailed answers in the stack overflow like this one which is color coded each one:

How to remove the left and right Padding of a List in SwiftUI?