Is there any way to instruct the model binder to recreate the Currency object when a different option item is selected on the client?

You can add hidden fields in the form to pass the properties of Currency like:

        <select id="currencySelect" class="form-select" asp-for="MyModel.Currency" onchange="updateCurrencyFields()">
            @foreach (var currency in Model.AllCurrencies)
            {
                if (currency.Code == Model.MyModel.Currency.Code)
                {
                    <option value="??????" data-numericcode="@currency.NumericCode"
                            data-code="@currency.Code" data-name="@currency.Name" selected="">
                        @currency.Name
                    </option>
                }
                else
                {
                    <option value="??????" data-numericcode="@currency.NumericCode"
                            data-code="@currency.Code" data-name="@currency.Name">
                        @currency.Name
                    </option>
                }
            }
        </select>
        <input type="hidden" asp-for="MyModel.Currency.NumericCode" id="NumericCode" />
        <input type="hidden" asp-for="MyModel.Currency.Code" id="Code"/>
        <input type="hidden" asp-for="MyModel.Currency.Name" id="Name"/>
    </div>
    <button type="submit">Submit</button>
</form>

<script>
    function updateCurrencyFields() {
        var select = document.getElementById("currencySelect");

        var numericcode = select.options[select.selectedIndex].getAttribute("data-numericcode");
        var code = select.options[select.selectedIndex].getAttribute("data-code");
        var name = select.options[select.selectedIndex].getAttribute("data-name");

        document.getElementById("NumericCode").value = numericcode;
        document.getElementById("Code").value = code;
        document.getElementById("Name").value = name;
    }
</script>

And code in the MyCurrencyPageModel like:

public class MyCurrencyPageModel : PageModel
{
    private readonly ApplicationDbContext _context;
    public MyCurrencyPageModel(ApplicationDbContext context)
    {
        _context = context;
    }

    [BindProperty]
    public MyModel MyModel { get; set; }

    public IEnumerable<Currency> AllCurrencies { get; set; }

    public void OnGet()
    {
        AllCurrencies = _context.Currencies.ToList();
        MyModel = new MyModel(Guid.NewGuid(), "Example Program", "Description", AllCurrencies.First());
    }

    public IActionResult OnPost()
    {
        if (!ModelState.IsValid)
        {
            return Page();
        }

        MyModel.Id = Guid.NewGuid(); 

        var item = _context.Currencies.Where(v=>v.Code ==MyModel.Currency.Code).FirstOrDefault();
        MyModel.Currency = item;

        _context.MyModels.Add(MyModel);
        _context.SaveChanges();

        return RedirectToPage("Index");
    }
}

With the test result: