build: unify the gate so root make check covers the backend (closes #16)

Root `make check` only ever ran the frontend, so the "main is always
green" policy was satisfied vacuously: the Go backend could be entirely
broken and the root gate stayed green.

- The backend moves onto scripts-to-rule-them-all. Its test, lint, fmt,
  fmt-check, build, run and clean implementations now live in
  `backend/script/`, and `backend/Makefile` is thin shims. The backend
  is its own project (own module, README, LICENSE, linter config,
  Dockerfile stage), and `Dockerfile.backend` only copies `backend/`
  into its builder, so its scripts have to live under `backend/`.
- The root `script/test`, `script/lint`, `script/fmt` and
  `script/fmt-check` now run the frontend step and then the matching
  `backend/script/*` step, so `script/check` — and therefore the
  pre-commit hook — gates both halves. The frontend-only steps moved
  into `script/frontend-*` so nothing is duplicated.
- `script/bootstrap` now provisions the backend's toolchain as well,
  because widening the gate without widening bootstrap left the
  documented fresh-clone path (`make setup`) installing a pre-commit
  hook that rejected every commit with `golangci-lint: not found`. Go
  is reused when the installed version is new enough, otherwise it is
  installed from the official `go1.25.7` release archive; golangci-lint
  is installed at exactly `2.7.2`, the version `Dockerfile.backend`
  pins, so local findings match CI. Both come from a specific release
  archive whose sha256 is hardcoded here and verified before anything
  is unpacked — never an install script piped to a shell — and both are
  symlinked onto `PATH`, since nvm-style activation does not reach
  `make` or the git hook.
- `script/frontend-check` is the frontend half of the gate, exposed as
  the `frontend-check` target, for the frontend Dockerfile: its build
  stage is a node image with no Go toolchain. The backend half is gated
  by `Dockerfile.backend`, and `script/cibuild` builds both images, so
  the two Dockerfiles together still gate the whole repo. The
  `backend-check` target is the mirror of it. Both targets are named
  after the script they shim, like every other target.
- `script/cibuild` builds both images through one `build_image` helper,
  and the Gitea workflow's only build step is `script/cibuild`; the raw
  `docker build -f Dockerfile.backend .` is gone from the workflow.
  `script/docker` likewise builds and tags both images.
- `backend/Makefile`'s `hooks` target is removed. It wrote the same
  `.git/hooks/pre-commit` as `script/install-precommit`, so the two
  clobbered each other and the developer silently ended up gating on
  only one half of the repo. `script/install-precommit` is now the only
  installer, and the hook it writes runs the repo-wide `script/check`.
- `backend/Makefile`'s `docker` target is removed too: the backend image
  builds from the repo root with a root-level Dockerfile, so it belongs
  to the root `script/docker` and `script/cibuild` rather than to a
  backend script that would have to reach outside `backend/`.
- `backend/script/lint` verifies that `.golangci.yml` still matches its
  pinned sha256 before running the linter. Offline hash comparison, no
  network. The pin is marked provisional in the file: it is the config
  currently on `main`, and the comment names PR #31 and the canonical
  hash that must replace it when #31 lands.
- Every script locates the repo root with the mandated
  `$(cd "$(dirname "$0")/.." && pwd -P)` idiom, `cd`s there, and calls
  siblings as `"$ROOT/script/<name>"`; the `SCRIPT_DIR` variant is gone.

READMEs at the root and in `backend/` document every script, the
backend's Getting Started separates commands run from `backend/` from
those run at the repo root, and `TODO.md` records the change.

script/precommit

@@ -3,10 +3,11 @@
 # checks fail. Our own extension to scripts-to-rule-them-all.
 set -eu
 
-SCRIPT_DIR="$(cd "$(dirname "$0")" && pwd -P)"
+ROOT="$(cd "$(dirname "$0")/.." && pwd -P)"
 
 main() {
-    "$SCRIPT_DIR/check"
+    cd "$ROOT"
+    "$ROOT/script/check"
 }
 
 main "$@"