Give the webhook handler a timeout (closes #38)

The webhook handler's client had no timeout, and slog calls the handler
inside the log call, so a server that accepted the connection and never
answered stopped that log call for good, and every later one. A request
still running after 5 seconds, reading the answer included, now fails
with a timeout error. The handler also reads the answer to the end
before closing it, so the connection is reused for the next record.

Two new tests point the handler at a server that never answers and at
one that sends its status and then stalls the answer, and check that
Handle returns a timeout error within the timeout. The README states
the timeout.

Model: opus-5-5

TODO.md

@@ -24,6 +24,9 @@ files it depends on: .golangci.yml, REPO_POLICIES.md, .editorconfig,
 
 # Completed Steps
 
+* 2026-10-06: a webhook request now times out after 5 seconds, so a
+    server that never answers no longer stops every log call; the webhook
+    handler also reads each answer to the end so its connection is reused
 * 2026-10-06: the tests run under the race detector, in Docker:
     `script/test` builds the `test` stage of the `Dockerfile`, which runs
     `go test -race`, and a new final stage makes a plain `docker build`