[ilyaZar]

The dev run after #5 failed in tests/logs.spec.mjs (expected 1 log read after close, got 2) with code identical to the passing PR head.

• page.clock.install() lets time flow, so on a slow runner the 2 s poll fires around the Close click and its request reaches the route after the test has taken its count
• the clock is now paused and advanced explicitly, with a check that polling runs while the dialog is open
• the negative check waits briefly for a late request; without that the test also passed with the cleanup removed from useLogTail (verified locally, it now fails with 2 vs 3)

Local: 20/20 repeated runs pass; lint, types and unit tests pass.