普通にConvert.ToStringを使えばいい
自作しなくちゃいけないならこう

public static string ToBinaryString(this uint source)
{
var length = sizeof(uint) * 8;
var result = new char[length].AsSpan();
for (int i = 1; i <= length; i++, source >>= 1)
{
result[^i] = (char)('0' + (source & 1));
}
return new string(result);
}