Serve ihasmail from a subpath

`BASE_PATH=/mail` mounts the whole app under a prefix, for a host that is not
ihasmail's alone. Unset -- every deployment that exists -- is the domain root
and is byte-for-byte what it was: the canonical form of the setting is the
empty string, and `""` concatenated onto `/api/health` is `/api/health`.

That choice of canonical form is the whole design. A trailing slash would have
been the obvious alternative, and it fails quietly in exactly one place: at the
root it makes `//api/health`, which is not a path on this host but a
protocol-relative URL to a host called `api`. One call site forgetting to
branch is a request leaving the origin. So the empty string, one leading slash,
no trailing one, worked out once in `scripts/basePath.mjs` -- plain JS, next to
`version.mjs`, because the web build and the server both have to reach the same
answer and two implementations of "what does /mail/ mean" is precisely the bug
where the server serves an app whose script tags point somewhere else.
`/mail`, `mail`, `/mail/` and `//mail//` all mean the same mount; a deployment
should not fail over a trailing slash.

Unlike everything else ihasmail is told, this one cannot wait for the process
to start. The bundle writes its own asset URLs into index.html, so `BASE_PATH`
is read at build time for Vite's `base` as well as at run time for the routes,
and the Dockerfile carries one value into both. Get them out of step and the
page comes up blank with a 404 in a console nobody has open -- so the static
handler, which is reading index.html anyway, checks what it asks for and says
so in the log once per build.

Everything moves together. The API mounts at `${base}/api`; the router is
given the base once, so every `<Route path>` and `<Link href>` stays written
root-absolute and wouter does the rest; `apiFetch` adds the prefix in one place
rather than at forty call sites; the session cookie's Path narrows to the mount
so two instances on one host cannot sign each other out.

Two things need no prefix at all, and it is worth saying why they were not
given one. A manifest's members resolve against the manifest's own address, so
relative URLs there follow the mount with nothing substituted at build time --
which is also why `public/` needed no template step. The service worker is the
same trick: it is served from the mount, so `new URL("./", self.location)`
tells it where that is, and a worker that derives the value cannot disagree
with the page that registered it.

Anything outside the mount is a 404 rather than the app shell, and
`stripBasePath` does not use `startsWith` -- under `/mail` this process shares
a hostname, and answering `/mailbox` with our index would shadow a neighbour
instead of letting it 404 honestly. For the same reason the notification-click
handler now checks the path as well as the origin: `includeUncontrolled` widens
`matchAll` to the whole origin, which off the root would have navigated a
stranger's tab to our inbox.

Inline images in a draft were the one silent trap. They are matched by their
blob URL on the way out, once unanchored and once anchored, and a bare
`/api/blob/` still appears inside `/mail/api/blob/...` -- so one pattern would
have replaced the tail and left `/mail` in front of a `cid:`, and the other
would have missed and sent the message linking to the sender's own webmail.
Both patterns are built from the base now.

server/src/basepath.test.ts

@@ -0,0 +1,63 @@
+import { test } from "node:test";
+import assert from "node:assert/strict";
+process.env.STALWART_URL = "http://127.0.0.1:1";
+const { createApp } = await import("./app.js");
+
+/**
+ * `BASE_PATH` is read once, into `config`, so these mount the app by argument
+ * instead of re-importing the module with a different environment. The
+ * root-mounted half is the one that matters most: every instance in existence
+ * is at `/`, and this feature has to be invisible to them.
+ */
+
+test("at the root, the API is exactly where it was", async () => {
+  const app = createApp("");
+  const res = await app.request("/api/health");
+  assert.equal(res.status, 200);
+});
+
+test("under a prefix, the API moves with it", async () => {
+  const app = createApp("/mail");
+  const res = await app.request("/mail/api/health");
+  assert.equal(res.status, 200);
+  const body = (await res.json()) as { ok?: boolean };
+  assert.equal(body.ok, true);
+});
+
+test("under a prefix, the unprefixed API is gone", async () => {
+  // Not merely unrouted: a proxy that forwards without the prefix, against a
+  // server told to expect one, would otherwise appear to half-work -- the API
+  // answering while the app shell it belongs to 404s.
+  const app = createApp("/mail");
+  const res = await app.request("/api/health");
+  assert.equal(res.status, 404);
+});
+
+/*
+ * Whether a route reached the static handler, without depending on there being
+ * a web build in the tree. With one it serves the index; without one it says
+ * the build is missing. Either is proof the request got that far -- a routing
+ * mistake is the 404, and asserting on 200 or 503 would make these tests pass
+ * or fail on whether somebody had run `npm run build` first.
+ */
+const reachedTheApp = (status: number) => status === 200 || status === 503;
+
+test("a deep SPA route under the prefix reaches the static handler", async () => {
+  const app = createApp("/mail");
+  const res = await app.request("/mail/calendar/week/2026-09-01");
+  assert.ok(reachedTheApp(res.status), `expected the app shell, got ${res.status}`);
+});
+
+test("a path that only shares the prefix's letters is not the app", async () => {
+  // `/mailbox` under a `/mail` mount belongs to whatever else the proxy
+  // serves on this host; answering it with our shell would shadow it.
+  const app = createApp("/mail");
+  assert.equal((await app.request("/mailbox")).status, 404);
+  assert.equal((await app.request("/")).status, 404);
+});
+
+test("the root mount still serves the SPA from the root", async () => {
+  const app = createApp("");
+  assert.ok(reachedTheApp((await app.request("/calendar/week/2026-09-01")).status));
+  assert.ok(reachedTheApp((await app.request("/")).status));
+});