build: run the browser e2e suites in CI (closes #259)

Nothing automatic ran either e2e suite, so every browser-level guarantee in this
wallet -- WebAssembly under the shipped CSP, the recovery-phrase and private-key
DOM wipes, the ConfirmTx spend gate, the dApp approval round trips -- held only
when a human or an agent remembered to run it by hand.

.gitea/workflows/e2e.yml adds two jobs, e2e-chrome and e2e-firefox, one per
browser so a Chrome failure cannot hide the Firefox result. They are separate
from the check workflow: REPO_POLICIES.md caps make test at 20 seconds and
script/cibuild is a docker build whose Dockerfile runs make check, so neither the
cap nor the local fast path is touched. make check is byte-for-byte unchanged.

Neither suite could run on the runner as it stood, and the reason is not
docker-in-docker. The runner executes a job inside a container against the HOST's
docker daemon, and the job's checkout lives on a docker volume rather than a host
path, so `docker run -v "$PWD:/work"` is resolved by the host, silently succeeds
and mounts an empty directory -- measured on this runner. The runner image's node
is also too old to install this repo's dependencies. Both suites therefore ship
the repo to the daemon as a build context and build the extension inside the
pinned image, which leaves docker as the only prerequisite on a runner or a
laptop. The suites themselves are unchanged; only how the repo reaches the
container is.

Both scripts now build with --iidfile and run the image by ID rather than by tag,
so two clones running a suite at once on the same host cannot swap it under each
other.

The jobs report, they do not gate. Whether a check blocks a merge is Gitea branch
protection, which this repo does not configure, so a failure is a red mark a
reviewer must account for. Nothing can pass vacuously: no continue-on-error, no
`|| true`, and both scripts exit non-zero when docker is missing, when the image
build fails and when the browser fails to start.

tests/e2e/Dockerfile

@@ -0,0 +1,34 @@
+# Chrome end-to-end image: the pinned Playwright image with this repo and a
+# freshly built extension inside it, built by script/test-e2e. The suite is
+# still started with `docker run`, so every runtime flag the harness needs
+# (--ipc=host in particular) applies as before.
+#
+# The repo is baked in rather than bind-mounted because a bind mount does
+# not resolve under Gitea Actions: the runner runs the job in a container
+# against the HOST's docker socket, so the source side of a -v is resolved
+# by the host daemon while the job's checkout lives on a docker volume that
+# is not a host path -- the mount silently succeeds and /work is empty. A
+# build context is streamed to the daemon and so works from anywhere.
+# Building the extension here too means the machine starting a run needs
+# docker and nothing else.
+
+# mcr.microsoft.com/playwright:v1.56.0-noble, 2026-08-09
+#
+# The playwright-core devDependency is pinned to the matching Playwright
+# version (1.56.0) and the two must be bumped together: the browsers ship
+# inside this image, and playwright-core looks for the exact browser
+# revision its own version expects. A mismatch fails at launch.
+FROM mcr.microsoft.com/playwright@sha256:35246d87a7c88ea9b771c65d33171b2611b02a8253b4b12ce6f94376c55f99f2
+
+WORKDIR /work
+
+# Same layering as the root Dockerfile: script/bootstrap installs the
+# prerequisites and the dependencies, and the manifests are copied first so
+# that layer is cached until they change.
+COPY script/ script/
+COPY package.json yarn.lock ./
+RUN script/bootstrap
+
+COPY . .
+
+RUN make build