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.

script/bootstrap

@@ -19,6 +19,7 @@ YARN_VERSION="1.22.22"
 
 PKGMGR=""
 SUDO=""
+APT_UPDATED=""
 
 detect_pkgmgr() {
     [ -n "$PKGMGR" ] && return 0
@@ -42,12 +43,24 @@ detect_pkgmgr() {
     fi
 }
 
+# A fresh Debian image ships no package lists at all, so apt-get install
+# fails with "E: Unable to locate package make" until they are fetched.
+# Done once per run, since the lists do not go stale mid-bootstrap.
+apt_update_once() {
+    [ -n "$APT_UPDATED" ] && return 0
+    $SUDO env DEBIAN_FRONTEND=noninteractive apt-get update
+    APT_UPDATED="yes"
+}
+
 # pkg_install <nix-attr> <apt-pkg> <brew-formula> <apk-pkg>
 pkg_install() {
     detect_pkgmgr
     case "$PKGMGR" in
         nix) nix-env -iA "nixpkgs.$1" ;;
-        apt) $SUDO env DEBIAN_FRONTEND=noninteractive apt-get install -y "$2" ;;
+        apt)
+            apt_update_once
+            $SUDO env DEBIAN_FRONTEND=noninteractive apt-get install -y "$2"
+            ;;
         brew) brew install "$3" ;;
         apk) apk add --no-cache "$4" ;;
     esac

script/cibuild

@@ -1,13 +1,17 @@
 #!/bin/sh
-# script/cibuild: run the CI build. The Dockerfile runs script/check, so
-# a successful build implies all checks pass.
+# script/cibuild: run the CI build. The Dockerfile runs script/check and
+# script/build, and CHECK_EPOCH differs on every invocation, so those two
+# layers cannot be served from Docker's cache: a green build here means
+# the checks ran now, not that a previous run was remembered. The layers
+# below the epoch (bootstrap, yarn install) are unaffected and stay
+# cached. A build that omits the argument fails by design.
 set -eu
 
 ROOT="$(cd "$(dirname "$0")/.." && pwd -P)"
 
 main() {
     cd "$ROOT"
-    docker build .
+    docker build --build-arg CHECK_EPOCH="$(date +%s)" .
 }
 
 main "$@"

script/docker

@@ -1,6 +1,9 @@
 #!/bin/sh
 # script/docker: build the Docker image tagged with the project name.
 # Identical in all repos; the tag comes from script/projectname.
+# CHECK_EPOCH is passed for the same reason script/cibuild passes it: the
+# Dockerfile refuses to build without it, so that no path to an image can
+# quietly serve the check and build layers from cache.
 set -eu
 
 SCRIPT_DIR="$(cd "$(dirname "$0")" && pwd -P)"
@@ -8,7 +11,8 @@ ROOT="$(cd "$SCRIPT_DIR/.." && pwd -P)"
 
 main() {
     cd "$ROOT"
-    docker build -t "$("$SCRIPT_DIR/projectname")" .
+    docker build --build-arg CHECK_EPOCH="$(date +%s)" \
+        -t "$("$SCRIPT_DIR/projectname")" .
 }
 
 main "$@"

script/projectname

@@ -6,7 +6,7 @@
 set -eu
 
 main() {
-    echo "quack"
+    echo "quak"
 }
 
 main "$@"