Make the image build multi-stage and cache-proof (closes #4)

The image build reported a green it had not earned. `script/cibuild` is a
bare `docker build .`, and with `COPY . .` followed by `RUN make check`,
an unchanged tree served that layer from cache: the suite never ran and
the build still exited 0, while the script's header comment asserted the
opposite.

CHECK_EPOCH, passed by `script/cibuild` and `script/docker`, changes the
cache key of the check and build layers on every invocation. It is
guarded, because an unset ARG is the empty string and therefore a stable
key: without the guard a plain `docker build .` — the command the policy
names, and the one anyone debugging types — would still get the false
green. A missing argument is now a hard failure rather than a silent
degradation to the behaviour the epoch was added to prevent.

The Dockerfile is now two stages: `fmt-check` and `lint` run first, and
the check stage takes a `COPY --from=lint` dependency on them, so a
formatting mistake fails the build in seconds instead of racing the
suite to the finish. Both stages stay pinned to the same digest.

The remaining fixes are one-liners that had made the target unusable:
`script/projectname` still printed the pre-rename name, so `make docker`
tagged its image after a name this project dropped in May;
`script/bootstrap` installed without fetching apt's package lists, which
cannot work on a Debian base; and `.dockerignore` had drifted far enough
from `.gitignore` to ship a ~100 MB compiled binary and any agent
worktree under `.claude/` into the build context. The second of those is
a correctness problem, not a size one — vitest globs a copied worktree's
tests alongside the real ones and runs the suite twice over. `.gitignore`
itself stays in the context, because prettier reads it as a default
ignore file and dropping it would change what `make fmt-check` sees.

Dockerfile

@@ -1,11 +1,37 @@
-# node 22-alpine, 2026-02-22
-FROM node@sha256:e4bf2a82ad0a4037d28035ae71529873c069b13eb0455466ae0bc13363826e34
-
+# Lint stage — fast feedback on formatting and lint issues
+# node 22.22.0 on Alpine 3.23.3 (node:22-alpine), 2026-08-09
+FROM node@sha256:e4bf2a82ad0a4037d28035ae71529873c069b13eb0455466ae0bc13363826e34 AS lint
 WORKDIR /app
 COPY script/ script/
 COPY package.json yarn.lock ./
 RUN script/bootstrap
 COPY . .
+RUN make fmt-check
+RUN make lint
 
+# Check stage — the full suite and the build
+# node 22.22.0 on Alpine 3.23.3 (node:22-alpine), 2026-08-09
+FROM node@sha256:e4bf2a82ad0a4037d28035ae71529873c069b13eb0455466ae0bc13363826e34 AS check
+WORKDIR /app
+
+# Force BuildKit to run the lint stage before proceeding. Without this the
+# two stages run in parallel and a lint failure can lose the race.
+COPY --from=lint /app/yarn.lock /dev/null
+
+COPY script/ script/
+COPY package.json yarn.lock ./
+RUN script/bootstrap
+COPY . .
+
+# CHECK_EPOCH is a cache buster: without it Docker serves `make check` from
+# cache on an unchanged tree, the suite never executes, and the build still
+# exits 0. The guard makes an absent argument a hard failure — an unset ARG
+# is the empty string, which is a perfectly stable cache key, so a plain
+# `docker build .` would otherwise still get the false green. Fail closed.
+ARG CHECK_EPOCH
+RUN [ -n "$CHECK_EPOCH" ] || exit 1
 RUN make check
+
+ARG CHECK_EPOCH
+RUN [ -n "$CHECK_EPOCH" ] || exit 1
 RUN make build