#9302 Shorten the slowest CI legs: website build, format check, rewatch polling

The website build ran on every pull request: the check for changed docs always found the copied .gitkeep and the website branch's older docs. An empty cache entry keyed on the website commit and the docs hash now records each build, so the ARM job skips about 3.5 minutes when the docs match an earlier build.

The format check gives the same result on every platform but took 25 s on Windows and 18 s on macOS, both on the critical path.

The canonical suite is the slowest part of each platform's rewatch step, and its waits polled once a second, so each of its ~150 waits took up to a second too long. Timeouts stay in seconds. Locally, the passing watch tests took 3.7 s instead of 6.9 s, 0.5 s instead of 4.1 s and so on.