Как обрабатывать изменения локальной темы в WinUI3?

Использование TextFillColorPrimary напрямую переключает цвет границы. Таким образом, вам не нужно звонить UpdateBrush().

<UserControl
    x:Class = "TestWinUI3App.UserControl1"
    xmlns = "http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x = "http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:local = "using:ThemeTest"
    xmlns:d = "http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc = "http://schemas.openxmlformats.org/markup-compatibility/2006"
    mc:Ignorable = "d">

    <!--<UserControl.Resources>
        <ResourceDictionary>
            <ResourceDictionary.ThemeDictionaries>
                <ResourceDictionary x:Key = "Default">
                    <StaticResource x:Key = "BorderBrush" ResourceKey = "TextFillColorPrimaryBrush"/>
                </ResourceDictionary>
                <ResourceDictionary x:Key = "Light">
                    <StaticResource x:Key = "BorderBrush" ResourceKey = "TextFillColorPrimaryBrush"/>
                </ResourceDictionary>
                <ResourceDictionary x:Key = "Dark">
                    <StaticResource x:Key = "BorderBrush" ResourceKey = "TextFillColorPrimaryBrush"/>
                </ResourceDictionary>
            </ResourceDictionary.ThemeDictionaries>
        </ResourceDictionary>
    </UserControl.Resources>-->

    <StackPanel Orientation = "Vertical">
        <Button Content = "Switch theme" Tapped = "Button_Tapped"/>
        <Border x:Name = "Border" BorderThickness = "1" BorderBrush = "{ThemeResource TextFillColorPrimary}">
            <TextBlock Text = "Theme text"/>
        </Border>
    </StackPanel>
</UserControl>

ОБНОВИТЬ

Если вам нужно сделать это программно:

private void UpdateBrush()
{
    foreach (ResourceDictionary themeDictionary in Application.Current.Resources.MergedDictionaries.Select(x => x.ThemeDictionaries))
    {
        ResourceDictionary? targetDictionary = null;

        if (themeDictionary.TryGetValue(RequestedTheme.ToString(), out var requestedThemeDictionary) is true)
        {
            targetDictionary = requestedThemeDictionary as ResourceDictionary;
        }
        else if (themeDictionary.TryGetValue(ElementTheme.Default.ToString(), out var defaultThemeDictionary) is true)
        {
            targetDictionary = defaultThemeDictionary as ResourceDictionary;
        }

        if (targetDictionary?.TryGetValue("TextFillColorPrimary", out object resource) is true &&
            resource is Color color)
        {
            Border.BorderBrush = new SolidColorBrush(color);
        }
    }
}

Для расширения разметки ThemeResource, которое использует процессор XAML, нет представления поддерживающего класса, но вы должны иметь возможность получить ссылку на словарь темы и получить оттуда ресурс:

private void Button_Tapped(object sender, TappedRoutedEventArgs e)
{
    RequestedTheme = RequestedTheme == ElementTheme.Dark ? ElementTheme.Light : ElementTheme.Dark;
    UpdateBrush();
}

private void UpdateBrush()
{
    var themeDictionary = Resources.ThemeDictionaries[ActualTheme.ToString()] as ResourceDictionary;
    Border.BorderBrush = themeDictionary["BorderBrush"] as SolidColorBrush;
}

Мое решение состояло в том, чтобы реализовать статический стиль в XAMl, который был назначен в C#:

XAML

<UserControl
    x:Class = "TestWinUI3App.UserControl1"
    xmlns = "http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x = "http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d = "http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc = "http://schemas.openxmlformats.org/markup-compatibility/2006"
    mc:Ignorable = "d">

    <UserControl.Resources>
        <Style x:Key = "BorderStyle" TargetType = "Border">
            <Setter Property = "BorderBrush" Value = "{ThemeResource TextFillColorPrimary}"/>
        </Style>
    </UserControl.Resources>

    <StackPanel Orientation = "Vertical">
        <Button Content = "Switch theme" Tapped = "Button_Tapped"/>
        <Border x:Name = "Border" BorderThickness = "1">
            <TextBlock Text = "Theme text"/>
        </Border>
    </StackPanel>
</UserControl>

С#

using Microsoft.UI.Xaml;
using Microsoft.UI.Xaml.Controls;
using Microsoft.UI.Xaml.Input;

namespace TestWinUI3App
{
    public sealed partial class UserControl1 : UserControl
    {
        public UserControl1()
        {
            InitializeComponent();
            Border.Style = Resources["BorderStyle"] as Style;
        }

        private void Button_Tapped(object sender, TappedRoutedEventArgs e)
        {
            RequestedTheme = RequestedTheme == ElementTheme.Dark ? ElementTheme.Light : ElementTheme.Dark;
        }
    }
}