Add playback source probing and integrate into player #6215

Job	Run time
Lint (Biome)	12s
Detect Changes	5s
Format (Biome)	7s
Typecheck	1m 33s
Format (Cargo)	17s
Rust cache (aarch64-apple-darwin, macos-latest)	6m 54s
Rust cache (x86_64-pc-windows-msvc, windows-latest)	6m 40s
Rust cache (x86_64-apple-darwin, macos-latest)	2m 43s
Build Desktop	-1s
Clippy	-1s
Verify Tauri plugin versions	-1s
	18m 28s

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