Prefetch display and window queries on mount #5386

Job	Run time
Detect Changes	5s
Format (Cargo)	9s
Lint (Biome)	13s
Format (Biome)	8s
Typecheck	38s
Rust cache (x86_64-pc-windows-msvc, windows-latest)	23s
Rust cache (x86_64-apple-darwin, macos-latest)	21s
Rust cache (aarch64-apple-darwin, macos-latest)	21s
Verify Tauri plugin versions	-1s
Build Desktop	-1s
Clippy	-1s
	2m 15s

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