Taskbar on multiple windows monitors - some switch, some stay in the old mode (x64)

### Description

When it swtches from light to dark, my external monitor task bar goes dark, but my main display stays light. The taskbard text also goes into darkmode so I can't read it.

### Expected Behavior

All taskbars on all monitors should go light or dark together

### Log Data

2025-12-08 14:26:25 | Info | PostponeManager.Remove: postpone queue cleared
2025-12-08 14:26:25 | Info | SystemEventHandler.SystemEvents_Windows11_SessionSwitch: system unlocked, refreshing theme
2025-12-08 16:11:50 | Info | ComponentManager.GetComponentsToUpdate: components queued for update: [AppsSwitch, SystemSwitch, WallpaperSwitch]
2025-12-08 16:11:50 | Info | ThemeFile.SyncWithActiveTheme: theme used for syncing is ADMTheme, path: C:\Users\nelsn\AppData\Local\Microsoft\Windows\Themes\ADMTheme.theme
2025-12-08 16:11:50 | Info | AppsSwitch.HandleSwitch: update info - previous: Light, pending: Dark, mode: Switch
2025-12-08 16:11:50 | Info | SystemSwitch.SwitchSystemTheme: update info - previous: Light, pending: Dark, mode: Switch, accent: no
2025-12-08 16:11:50 | Info | WallpaperSwitch.LogHandleSwitch: update info - previous: Light/Fill, now: Dark/Fill, mode: Fill, type: SolidColor
2025-12-08 16:11:52 | Info | Tm2Handler.SetTheme: applied theme ADMTheme, from origin: C:\Users\nelsn\AppData\Local\Microsoft\Windows\Themes\ADMTheme.theme directly via IThemeManager2
2025-12-08 16:11:52 | Info | ThemeManager.UpdateTheme: dwm management: provided refresh type none insufficent, minimum: standard
2025-12-08 16:11:52 | Info | ThemeManager.UpdateTheme: dark theme switch performed, source: TimeSwitchModule, sunset: 12/7/2025 4:11:43 PM
2025-12-08 16:11:54 | Info | DwmRefreshHandler.Broadcast: dwm management: starting broadcast
2025-12-08 16:11:54 | Info | DwmRefreshHandler.Broadcast: dwm management: refresh complete
2025-12-08 17:30:08 | Info | PostponeManager.Remove: postpone queue cleared
2025-12-08 17:30:08 | Info | SystemEventHandler.SystemEvents_Windows11_SessionSwitch: system unlocked, refreshing theme
2025-12-08 18:26:16 | Info | LocationHandler.UpdateWithGeolocator: updated geoposition via geolocator
2025-12-08 18:26:16 | Info | LocationHandler.UpdateSunTime: new sunrise (07:01) and new sunset (16:11)
2025-12-08 18:48:42 | Info | MessageParser.Parse: signal received: request for running status
2025-12-08 18:48:42 | Info | MessageParser.Parse: signal received: validate autostart entries
2025-12-08 18:48:42 | Info | TaskSchdHandler.GetLogonTask: logon task folder does not exist

### Commit Hash, Version and Windows Build

- Commit: `5678573e`
- Service/App: `11.0.0.54`
- Updater: `4.0.3`
- Shell: `1.3.3.0`
- .Net: `9.0.8`
- Windows: `26200.7309`
- Arch: `X64`

### Screenshots / Videos

Start by reproducing the light-to-dark switch on multiple monitors and read the logged path through SystemSwitch.SwitchSystemTheme, Tm2Handler.SetTheme, and DwmRefreshHandler.Broadcast. Compare the refresh behavior for each taskbar; done means all monitor taskbars change mode together and their text remains readable.

Written by the indexing model from the issue text.