Can I limit the use of a widget based on a specific page type?

I don't think you can directly restrict a widget to a specific Content Type, but you can restrict them in the View used for the Page Type's template. I believe there's a couple ways of approaching it:

You can restrict widgets for editable areas:

<div>
    @{
        var optionsLimited = new EditableAreaOptions
        {
            AllowedWidgets = new[] { "LearningKit.Widgets.NumberWidget",
                                     "LearningKit.Widgets.SomeOtherWidget" },
            AllowedSections = AllowedComponents.ALL
        };
    }
    @await Html.Kentico().EditableAreaAsync("limitedArea", optionsLimited)
</div>

You can restrict widgets for widget zones:

<div>
    @{
        var widgetsAllowlist = new[] { Kentico.Content.Web.Mvc.SystemComponentIdentifiers.FORM_WIDGET_IDENTIFIER,
                                       "LearningKit.Widgets.NumberWidget",
                                       "LearningKit.Widgets.SomeOtherWidget" };
    }
    @await Html.Kentico().WidgetZoneAsync(allowedWidgets: widgetsAllowlist)
</div>