feat(examples): add Context API state management example #7989

Job	Run time
Check MSRV	35s
Check	4m 55s
cargo test \| windows	9m 51s
Clippy	1m 45s
Docs	1m 54s
Rustfmt	26s
matrix_test (aarch64-apple-darwin, macos-latest, 1.84.0, false, test, --all --tests)	4m 6s
nix (ubuntu-latest)	7m 1s
Playwright Tests	5m 28s
matrix_test (x86_64-apple-darwin, macos-13, 1.84.0, false, test, --all --tests)	6m 45s
nix (macos-latest)	10m 1s
matrix_test (aarch64-apple-ios, macos-latest, 1.84.0, false, build, --package dioxus-mobile)	50s
matrix_test (aarch64-linux-android, ubuntu-latest, 1.84.0, true, build, --package dioxus-mobile)	1m 33s
Test Suite with Optimizations	4m 49s
Test Suite	5m 49s
	1h 5m 48s

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