[SampleApp] Preserve launch metadata and window placement across theme switches

[Anna Malchow-Perryman (apman)]

Summary

• keep SampleApp title metadata stable across theme-triggered window recreation by caching launch time and launch branch once per process
• preserve window placement when recreating MainWindow on theme changes (position, size, and window state)
• avoid reopening on the primary display by forcing manual startup location when applying saved placement

Why

Switching themes intentionally recreates the window. Before this change, that caused:

• title branch/time to refresh to current values instead of original launch values
• the recreated window to jump back to the laptop/primary monitor

This PR keeps both pieces of context stable across theme switches.

Validation

• dotnet test passed (124/124)

Notes

• minimized state is not carried across recreation; it restores as Normal to avoid reopening minimized.

[Copilot]

Pull request overview

This PR improves the SampleApp’s theme-switch experience by keeping launch metadata (branch/time) stable across window recreation and restoring the window’s previous placement when MainWindow is recreated due to a theme change.

Changes:

• Cache launch time and git branch once per process so the title doesn’t refresh on theme-triggered window recreation.
• Capture and reapply window placement (position, size, window state) when recreating MainWindow during theme changes.
• Force WindowStartupLocation.Manual on recreation to avoid reopening centered on the primary display.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated no comments.

File	Description
samples/SampleApp/MainWindow.axaml.cs	Caches launch time/branch and reuses them when rebuilding the window title after theme-driven recreation.
samples/SampleApp/App.axaml.cs	Captures old window placement and applies it to the newly created MainWindow to preserve monitor/size/state across theme switches.

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