Similar in behaviour to the navigationTitle, I woul like the category names e.g. "Data #1" to remain at the top of the screen, untul the next category in the ScrollView meets to replace it (similar to the date label grouping chat messages in WhatsApp will change as the next group scrolls up).

import SwiftUI

let dataSet: [Data] = [

    // DATA #1
    Data(info: "Info #1A", category: .data1),
    Data(info: "Info #1B", category: .data1),
    Data(info: "Info #1C", category: .data1),
    Data(info: "Info #1D", category: .data1),
    Data(info: "Info #1E", category: .data1),
    Data(info: "Info #1F", category: .data1),

    // DATA #2
    Data(info: "Info #2A", category: .data2),
    Data(info: "Info #2B", category: .data2),
    Data(info: "Info #2C", category: .data2),
    Data(info: "Info #2D", category: .data2),
    Data(info: "Info #2E", category: .data2),
    Data(info: "Info #2F", category: .data2),

    // DATA #3
    Data(info: "Info #3A", category: .data3),
    Data(info: "Info #3B", category: .data3),
    Data(info: "Info #3C", category: .data3),
    Data(info: "Info #3D", category: .data3),
    Data(info: "Info #3E", category: .data3),
    Data(info: "Info #3F", category: .data3),

    // DATA #4
    Data(info: "Info #4A", category: .data4),
    Data(info: "Info #4B", category: .data4),
    Data(info: "Info #4C", category: .data4),
    Data(info: "Info #4D", category: .data4),
    Data(info: "Info #4E", category: .data4),
    Data(info: "Info #4F", category: .data4),

    // DATA #5
    Data(info: "Info #5A", category: .data5),
    Data(info: "Info #5B", category: .data5),
    Data(info: "Info #5C", category: .data5),
    Data(info: "Info #5D", category: .data5),
    Data(info: "Info #5E", category: .data5),
    Data(info: "Info #5F", category: .data5),
]

enum DataCategory: String, CaseIterable {
    case data1 = "Data #1"
    case data2 = "Data #2"
    case data3 = "Data #3"
    case data4 = "Data #4"
    case data5 = "Data #5"
}

struct Data: Identifiable {
    let id = UUID()
    let info: String
    let category: DataCategory
}

struct TileTitleTestView: View {

    var body: some View {
        VStack {
            Text("default")
                .padding()
                .cornerRadius(8)
        }
        .frame(maxWidth: .infinity)
        .background(Color.blue)
        .foregroundColor(.white)
        .cornerRadius(15)
        .padding(5)
    }
}

struct TileArrayView: View {
    let data: [Data]

    var body: some View {
        ScrollView {
            LazyVGrid(columns: Array(repeating: GridItem(.flexible(), spacing: 10), count: 3), spacing: 10) {
                ForEach(DataCategory.allCases, id: \.self) { category in
                    Section(header:
                                Text(category.rawValue)
                                    .font(.system(size: 30).bold())
                                    .multilineTextAlignment(.leading)
                                    .foregroundColor(.black)
                    ) {
                        ForEach(data.filter { $0.category == category }) { data in
                            DataTile(data: data)
                                .aspectRatio(1, contentMode: .fit)
                        }
                    }
                }
            }
            .padding()
        }
    }
}

struct DataTile: View {
    let data: Data

    var body: some View {
        VStack {
            Text(data.info)
                .padding()
                .cornerRadius(8)
        }
        .frame(maxWidth: .infinity)
        .background(Color.pink)
        .foregroundColor(.black)
        .cornerRadius(15)
        .padding(5)
    }
}

As close as possible to the default behaviour of the navigationTitle, that will appear in the top centre title bar would be my goal.

Yes !

However, I would preffer the text to be backed by a white margin at the top, so the cells do not touch the title.

How do I achieve this please ?

As possible solution change your section header to this.

Section(header:
            Color.white
    .frame(height: 60)
    .overlay {
        Text(category.rawValue)
            .font(.system(size: 30).bold())
            .multilineTextAlignment(.leading)
            .foregroundColor(.black)
    }
)

Thank you very much once again !

This helps a lot with the effect: .statusBar(hidden: true)

Great to hear you solved it! If you have any further questions or need assistance with anything else, feel free to ask!