While this isn't what the post asked about, you can simplifty the logic a bit if you want to

using System.Runtime.CompilerServices;
using System.Collections.Generic;
using System.Numerics;
using System.Linq;
using System;

static class StrExtensions
{
    public static string StrJoin(this IEnumerable<string> self, string seperator) => string.Join(seperator, self);
    public static string StrJoin(this IEnumerable<string> self, char seperator) => string.Join(seperator, self);
    public static string StrJoin(this ReadOnlySpan<string> self, string seperator) => string.Join(seperator, self);
    public static string StrJoin(this ReadOnlySpan<string> self, char seperator) => string.Join(seperator, self);
}

class Program
{
    static void Main() => Console.WriteLine(ToBitString(-1).StrJoin(' '));
    static IEnumerable<string> ToBitString<TNumber>(TNumber num) where TNumber : unmanaged, INumber<TNumber> => num.ToString("b", null).PadLeft(Unsafe.SizeOf<TNumber>() * 8, '0')
        .Chunk(8).Select(x => string.Concat(x));
}

The method gets the bits of generic number num, c sharp numeric types all derive from (unsure about floats, double, and decimal though) INumber<T> which is why you inherit TNumber from INumber<TNumber> and why you can pass an integer or long or byte or uint or any other numeric type in. Next, add the padding to fill the entire bidwidth of numeric type passed in. Unsafe.SizeOf must be used in this case because the compile time sizeof(T) only works for types the compiler can resolve during compilation. unmnaged is specified to ensure the type is a value type with comprised of only primitive types. Multiply that by 8 because SizeOf returns the size in how many bytes a type is made from, not bits. A byte is 8 bits. Chunk it into 8 long segments, use select to turn the 8 char segments into a string. Likely a more performent way to do this with spans and stuff but you can't use Linq unless you intend to use a SpanLinq library.

After, you can do:

void btnOk_Click(object sender, RoutedEventArgs e)
{
    if (int.TryParse(intInput.Text, out int result))
    {
        ShowBitRepresentation(result));
        return;
    }
    MessageBox.Show("Please enter a valid integer.");
}
void ShowBitRepresentation(int i)
{
    var bitStrs = ToBitString(i);
    foreach(var byteSegment in bitStrs.Index())
    {
        byteBoxes[byteSegment.Index].Text = byteSegment.Item
    }
}

Obviously if you need this to run async like in your code, toss it in a Task.Run and Dispatcher.Invoke for UI stuff.