You cannot bind to other_object you can bind to a string property of other_object or use a TypeConverterAttribute to convert your other_object to a string.

Your code can be :

<select class="custom-select" @bind="@_selected.id">
     <option value="@object.apple.id">@object.apple.name</option>
     ...
</select>
@code {
    private other_object _selected = new other_object();
    ...
}

You can do it like this in case for any reason you need the object to be created here:

<InputSelect @bind-Value="@object.apple.id" @onchange="@((args) => @object.apple = new other_object { id = (int)args.Value })" class="form-control">
      <option value="@object.apple.id">@object.apple.name</option>                        
</InputSelect>

Here's a solution for binding an object to the <select> option in Blazor using @bind-Value:get and @bind-Value:set. In this example, we use <InputSelect> to bind the selected value to a selected property and define a SetSelected method to update the object object with the selected object from the ListOtherObjects list.

<InputSelect @bind-Value:get="selected" @bind-Value:set="SetSelected" class="form-control">
    <option value="">Select an option</option>
    @foreach (var value in ListOtherObjects)
    {
        <option value="@value.Id">@value.name</option>
    }
</InputSelect>

@code {
    private string selected = null!;
    private List<other_object> ListOtherObjects = new() { new() { id = 1, name = "name1" }, new() { id = 2, name = "name2" } };
    public object object { get; set; } = new();

    void SetSelected(string value)
    {
        var _ = ListOtherObjects.Find(e => e.Id == value);
        if (_ != null)
            object.apple = _;
        selected = value;
    }
}

I hope this solution helps you. If you have any questions or need more information, please let me know.