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.

.dockerignore

@@ -1,8 +1,50 @@
+# Mirrors .gitignore, with one deliberate exception: .gitignore itself stays
+# in the build context, because prettier 3 reads it as a default ignore file
+# and dropping it would change what `make fmt-check` sees inside the image.
+
+# VCS
 .git
+
+# OS
+.DS_Store
+Thumbs.db
+
+# Editors
+*.swp
+*.swo
+*~
+*.bak
+.idea/
+.vscode/
+*.sublime-*
+
+# Node
 node_modules
+
+# TypeScript / build artifacts
 dist
 build
+*.tsbuildinfo
 coverage
-.DS_Store
+.nyc_output/
+
+# Vitest
+.vitest-cache/
+
+# Environment / secrets
 .env
 .env.*
+*.pem
+*.key
+
+# Compiled binary (built by make build-bin); around 100 MB
+bin/quak
+
+# quak runtime data (in case anyone runs the CLI from inside the repo)
+.quak/
+
+# Local per-developer tool state, including agent worktrees. Correctness,
+# not context size: a worktree copied in here has its own test/ tree, which
+# vitest globs alongside the real one, so the containerised suite runs N+1
+# times over and still reports success.
+.claude/