Sorry for the slow repsonse but there is a quite alot of code. I will try to explain a few of the pionts.

You need to document your code so it easier to understand (you can use option+click to get a summary or drill down to the file quickly)

3 - You have groups the files with Model, Views, ViewModels, however (personal) I group them by view eg Start, Card etc with ALL the files that are used in that file so when you working on a view then find them easily! PS could not see any properties that did not have to in the ViewModel

4 - Had a look at one AddCardView and there quite alot of modifiers so I suggest that use of ViewModifliers.

Add a file I called it TextFieldViewModifier

struct TextFieldViewModifier: ViewModifier {
    @Environment(\.colorScheme) var colorScheme

    func body(content: Content) -> some View {
        content
            .padding()
            .border(LinearGradient.gradient(for: colorScheme))
    }
}

Also add a file called ButtonViewModifier

struct ButtonViewModifier: ViewModifier {
    @Environment(\.colorScheme) var colorScheme

    func body(content: Content) -> some View {
        content
            .padding()
            .padding(.horizontal)
            .foregroundStyle(Color.primary)
            .overlay {
                RoundedRectangle(cornerRadius: 10)
                    .stroke(LinearGradient.gradient(for: colorScheme), lineWidth: 2)
            }
    }
}

Now add a file Extension-View this will make the call site cleaner (note the documentation)

extension View {
    /// A modifier that give a gradient color border to a `TextField`.
    ///
    /// When applied it will change the border to a linear gradient from bottomTrailing to topLeading
    /// of [.pink, .purple, .black] or [.pink, .purple, .white] depending on light/dark mode.
    var textFieldViewModifier: some View {
        self.modifier(TextFieldViewModifier())
    }

    /// A modifier that give a gradient color `RoundedRectangle` to a `Button`
    ///
    /// When applied it will change the border to a linear gradient from bottomTrailing to topLeading
    /// of [.pink, .purple, .black] or [.pink, .purple, .white] depending on light/dark mode.
    var buttonViewModifier: some View {
        self.modifier(ButtonViewModifier())
    }
}

Now you can use in AddCardView (Also used Label in toolbar button - give accessibility label)

struct AddCardView: View {
    @EnvironmentObject var dataController: DataController
    @StateObject private var viewModel = ViewModel()
//    @Environment(\.colorScheme) var colorScheme
    @Environment(\.dismiss) var dismiss

    var body: some View {
        NavigationView {
            VStack {
                SecureField("Enter card number", text: $viewModel.cardNumber)
                    .keyboardType(.numberPad)
                    .textFieldViewModifier
//                    .foregroundColor(colorScheme == .light ? .black : .white) // ** NOT NEEDED **
//                    .padding()
//                    .border(LinearGradient.gradient(for: colorScheme))

                TextField("Enter balance", text: $viewModel.balance)
                    .keyboardType(.decimalPad)
                    .textFieldViewModifier
//                    .foregroundColor(colorScheme == .light ? .black : .white) // ** NOT NEEDED **
//                    .padding()
//                    .border(LinearGradient.gradient(for: colorScheme))

                Button { // ** YOU MIGHT WANT TO DISABLE BUUTON UNTIL CARD DETAILS AND AMOUNT ARE FILLED **
                    viewModel.maskCardNumber(dataController: dataController)
                    dismiss()
                } label: {
                    Text("Submit")
                        .buttonViewModifier
//                        .padding()
//                        .padding(.horizontal) // .horizontal same as [.leading, .trailing]
//                        .foregroundStyle(Color.primary) // use this it changes between black/white
//                        .foregroundColor(colorScheme == .light ? .black : .white)
//                        .overlay {
//                            RoundedRectangle(cornerRadius: 10)
//                                .stroke(LinearGradient.gradient(for: colorScheme), lineWidth: 2)
//                        }
                }
                .padding(.top)
//                .accessibilityLabel("Press this button for insert you card informations") // ** NO NEED AS "submit" IS BETTER **
                .accessibilityHint("Added!") // better to "this will add the new card"
                if !viewModel.errorMessage.isEmpty {
                    Text(viewModel.errorMessage)
                        .foregroundColor(.red)
                        .padding(.vertical)
                }
            }
            .padding()
            .toolbar {
                Button {
                    dismiss()
                } label: {
                    Label("Close", systemImage: "xmark.circle") // change to xmark.circle not x.circle
                        .symbolRenderingMode(.multicolor)
//                    Image(systemName: "x.circle")
//                        .foregroundColor(.red)
                }
//                .accessibilityLabel("Return to previous screen") // ** NO NEED AS USE OF LABEL **
            }
            .navigationTitle("Add Card")
            .navigationBarTitleDisplayMode(.inline)
        }
    }
}

By deleting the commented out code it will read easier.

I also noticed that the TextFields in WelcomeView and AddCardView are different. I would change the TextFieldViewModifier to

struct TextFieldViewModifier: ViewModifier {
    @Environment(\.colorScheme) var colorScheme

    func body(content: Content) -> some View {
        content
            .textFieldStyle(.roundedBorder)
            .overlay {
                RoundedRectangle(cornerRadius: 5)
                    .stroke(LinearGradient.gradient(for: colorScheme), lineWidth: 1)
            }
    }
}

now you can add this

Group {
    TextField("Name", text: $viewModel.firstName)
    TextField("Last Name", text: $viewModel.lastName)
}
.textFieldViewModifier

You could do the same with the button.

Just one other thing if you change LinearGradient to this (note .primary instead of .black/.white)

static var borderGradient: LinearGradient {
    LinearGradient(colors: [.pink, .purple, .primary], startPoint: .bottomTrailing, endPoint: .topLeading)
}

then every you used .gradient(for colorScheme: ColorScheme) you can use LinearGradient.borderGradient and not use colorScheme

struct TextFieldViewModifier: ViewModifier {
    func body(content: Content) -> some View {
        content
            .textFieldStyle(.roundedBorder)
            .overlay {
                RoundedRectangle(cornerRadius: 5)
                    .stroke(LinearGradient.borderGradient, lineWidth: 1)
            }
    }
}

Sent Pull Request on github of changes if you want to use it