Split test-examples into two phases: build all examples in parallel
first, then run tests serially against pre-built binaries. Abort on any
build failure instead of skipping tests for that example.

Replace the centralized `examples/test-examples.toml` with individual
`test.toml` files in each example directory, updating the test runner
and related documentation accordingly.

Replace the separate code/docs CI jobs and local check flags with
a unified `--check-*` flag system, enabling each check to run
independently across a platform matrix.

Replace relative file links with absolute URLs and add centered page
headers
to the migrated docs. Update the dev sidebar to include the new pages.