e2e: run health probe + Playwright on the compose network

Gitea's act-style runners execute workflow steps inside a runner
container, so compose's host port-publish (127.0.0.1:8080:8080) is
not reachable from the steps. PR #23's e2e job timed out waiting
for the server even though the container was up and listening.

Move both the health probe and the Playwright run onto rmnet so
they address the server as http://server:8080:

* health probe: docker run --rm --network e2e_rmnet curlimages/curl
* Playwright: new mcr.microsoft.com/playwright-based image, added
  as a profile-gated `playwright` service in compose.e2e.yml,
  invoked via `docker compose run --rm playwright`. Drops the
  setup-node + npm install runner steps.

e2e/Dockerfile.playwright

@@ -0,0 +1,21 @@
+# Playwright runner for the e2e suite. Built and run by
+# e2e/compose.e2e.yml so the test process sits on the same docker
+# network as the server, agent, and rest-server. The previous setup
+# ran Playwright on the workflow runner host and reached the server
+# via 127.0.0.1:8080; that fails on Gitea's act-style runners
+# because the workflow steps execute inside a runner container,
+# not on the host where compose publishes its ports.
+
+FROM mcr.microsoft.com/playwright:v1.50.0-jammy
+
+WORKDIR /work
+
+# Install npm deps in a separate layer keyed off package.json so
+# changes to specs don't bust the dep cache.
+COPY e2e/playwright/package.json /work/package.json
+RUN npm install --no-audit --no-fund
+
+COPY e2e/playwright/ /work/
+
+ENV CI=1
+ENTRYPOINT ["npx", "playwright", "test"]