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.

FEATURES.md

@@ -954,6 +954,7 @@ wizard, because either would be state.
 | `STALWART_URL` | — | Where Stalwart is; the JMAP session is discovered at `/.well-known/jmap` |
 | `APP_SECRET` | — | Key material for sealing sessions. **Required in production** — the server refuses to start without it |
 | `HOST` / `PORT` | `0.0.0.0` / `8080` | Listen address |
+| `BASE_PATH` | — (the domain root) | Subpath to serve from, e.g. `/mail`. Must be set for the **build** as well as the run — see below |
 | `TRUST_PROXY` | `1` | Believe `X-Forwarded-*` |
 | `TRUSTED_PROXIES` | loopback + private ranges | Which peers to believe |
 | `SECURE_COOKIES` | `auto` | `Secure` when the request arrived over HTTPS; `1`/`0` to force |
@@ -973,6 +974,41 @@ Full documentation, including TLS and reverse proxies:
 [Configuring](https://docs.ihasmail.org/configure/). `Caddyfile.example` and
 `nginx.example.conf` are in the repository.
 
+### Serving from a subpath
+
+`BASE_PATH` mounts the whole app under a prefix, for a host that is not
+ihasmail's alone:
+
+```bash
+docker build --build-arg BASE_PATH=/mail -t ihasmail .
+docker run -e BASE_PATH=/mail ... ihasmail
+```
+
+`/mail`, `mail` and `/mail/` all mean the same mount; unset means the domain
+root, which is exactly what it has always been. Everything moves together —
+`/mail/api/health`, every deep link, the icons, the manifest, the service
+worker's scope and the session cookie's `Path`.
+
+Two things are worth knowing before you reach for it.
+
+**The prefix must arrive intact.** Point the proxy at ihasmail without
+stripping it: `proxy_pass http://127.0.0.1:8080;` with no trailing slash in
+nginx, `reverse_proxy` without a `uri strip_prefix` in Caddy. A proxy that
+strips the prefix is talking to an app at the root, and should be paired with
+no `BASE_PATH` at all.
+
+**It is baked in at build time, not only at run time.** This is the one setting
+that cannot wait for the process to start: the web bundle writes its own
+`<script src>` into `index.html` when it is built, so a build that does not
+know the prefix produces a shell that cannot load itself under one. Hence the
+`--build-arg` above. Get it wrong and the page comes up blank — so the server
+checks the built shell against its own `BASE_PATH` at the first request and
+says so in the log rather than leaving you with an empty page and a 404.
+
+The manifest and the service worker need neither: a manifest's URLs resolve
+against the manifest's own address, and the worker's own address tells it where
+it was mounted. Both follow the prefix with nothing substituted into them.
+
 ## Rebranding
 
 `APP_NAME` and `SOURCE_URL` are variables; the logo, icons and palette are
@@ -984,7 +1020,8 @@ and in Settings › About.
 ## Operations
 
 - **`GET /api/health`** answers name, version and `ok`, and is what the
-  container health check uses.
+  container health check uses. Under a `BASE_PATH` it moves with everything
+  else, to `/mail/api/health`; the image's health check follows it.
 - **Versions** read `2026.8.30+pr129`: the date of the commit the build came
   from, and the pull request it arrived through (or `+g<sha>` for one that did
   not). It comes from git at build time; nothing writes a version into the tree.