docs: fix stale TLS/routing references (audit sweep)

Cross-checked every doc against the code and fixed the stragglers the
apply/gateway/subdomain refactors left behind:

- Retired `tls: internal` mode: dropped the misleading reference in
  registry.md and the stale comment in config.py GatewayConfig (only
  off|acme exist; the dns-and-tls.md "was removed" note is kept as
  accurate history).
- Subdomain-only routing: fixed "path-based routing" claims in design.md
  (proxy list + mesh), "path prefix or host" → host, and the "path-prefix
  routes stay on :port" line in registry.md.
- Frontends serve at their subdomain root (VITE_BASE=/), not /<name>/:
  fixed supabase.md (x2), the scaffold.py docstring, the stacks.py build
  comment, and design.md's "serve prefix baked in" line.

README, AGENTS, developing-castle, dns-and-tls audited clean. Verified
against code; core 129 / cli 31 pass; ruff clean.

docs/design.md

@@ -114,7 +114,8 @@ Manages running processes using standard Linux infrastructure.
 
 **Caddy** handles HTTP routing:
 - Reverse proxy on port 9000
-- Path-based routing to services (`/api` → port 9020)
+- Subdomain routing to services (`<service>.<domain>`); the `/api` path is
+  reserved for the dashboard's own backend in no-domain (HTTP-only) mode
 - Static file serving for frontends
 - TLS termination
 
@@ -131,7 +132,7 @@ infrastructure and gets out of the way.
 Systemd units point to installed binaries (on PATH or in `~/.local/bin/`),
 not to repo subdirectories. Frontends are the deliberate exception: rather
 than stage a copy, Caddy serves their built assets **in place** from the repo
-(`<source>/<dist>/`), with the serve prefix baked into the build via `VITE_BASE`.
+(`<source>/<dist>/`) at the root of its own subdomain (`VITE_BASE=/`).
 
 ### Registry Layer
 
@@ -258,7 +259,7 @@ programs on a single node and across multiple Castle nodes.
 
 **Intra-node coordination:**
 - Programs find each other through the gateway or direct port access via env
-  vars. A gateway route maps an address (path prefix or host) to a target of one
+  vars. A gateway route maps a host address (`<name>.<domain>`) to a target of one
   kind: **proxy** (a local service port), **remote** (a service on another
   node), or **static** (a built frontend's `dist/`, served as files). The same
   computed route list drives the Caddyfile, `castle gateway status`, and the
@@ -270,8 +271,9 @@ programs on a single node and across multiple Castle nodes.
 - Each Castle node runs the API, which exposes its program registry.
 - Nodes discover each other via MQTT retained messages and mDNS/DNS-SD
   (python-zeroconf) for LAN environments.
-- The gateway on each node can proxy to services on other nodes,
-  preserving path-based routing. Components don't know which node
+- The gateway on each node can proxy to services on other nodes via
+  host-based routing (`<service>.<domain>` resolves to the local port or,
+  via the remote registry, another node). Components don't know which node
   they're talking to.
 - MQTT provides pub/sub messaging for events, status, and coordination
   across nodes.

docs/registry.md

@@ -395,8 +395,8 @@ version number"). `gateway.tls` has two values:
 | `off` (default/unset) | `:<port>` HTTP, `auto_https off` | host matcher on `:<port>` | none |
 | `acme` | one `*.<domain>` `:443` site | matcher inside the wildcard site | **real Let's Encrypt wildcard, no CA install** |
 
-Path-prefix and static routes always stay on the HTTP `:<port>` site — the way to
-put a service on HTTPS is to set `proxy: true` (and use acme mode). A node with no public
+In `off` mode all routes stay on the HTTP `:<port>` site — the way to put a
+service on HTTPS is to set `proxy: true` (and use acme mode). A node with no public
 domain stays on `off` (plain HTTP; use `localhost`/direct ports for anything that
 needs a secure context).
 
@@ -413,9 +413,10 @@ the floor once: `net.ipv4.ip_unprivileged_port_start=80` (persist in
 
 #### Publicly-trusted HTTPS — `gateway.tls: acme`
 
-A private-CA approach (Caddy's `tls internal`) forces every client device to trust
-a custom root — which some platforms (e.g. Android browsers, and Firefox, which
-uses its own store) make painful. `acme` mode avoids it entirely: Caddy obtains a
+A private-CA approach would force every client device to trust a custom root —
+which some platforms (e.g. Android browsers, and Firefox, which uses its own
+store) make painful — so Castle doesn't offer one. `acme` mode avoids it entirely:
+Caddy obtains a
 **real Let's Encrypt wildcard cert** (`*.<domain>`) via a **DNS-01** challenge, so
 every browser trusts it with **zero CA install** — while the services stay
 **internal-only**.

docs/stacks/supabase.md

@@ -63,7 +63,7 @@ my-app/
 
 Registered as a program with `build.outputs: [public]` plus a `manager: caddy`
 deployment (`root: public`, derived **kind: static**), so the
-gateway serves `public/` in place at `/my-app/` — no service, no process.
+gateway serves `public/` in place at `<name>.<gateway.domain>` (its own subdomain root) — no service, no process.
 
 ## supabase.app.yaml
 
@@ -161,7 +161,7 @@ service itself is likewise at `supabase.<gateway.domain>`.) See
 castle program create my-app --stack supabase --description "..."   # scaffold + register
 castle program build my-app        # apply unapplied migrations to the substrate
 castle program test  my-app        # deno test over functions/ (if deno present)
-castle apply    # serve the static UI at /my-app/
+castle apply    # serve the static UI at <name>.<gateway.domain>
 ```
 
 ## Scaffolding

docs/tunnel-setup.md

@@ -143,7 +143,7 @@ Reachability is the easy half. Anything public also needs, per service:
 ## Notes
 
 - Requires `gateway.tls: acme` (the tunnel forwards to the gateway's real-cert
-  `:443` host sites). On an `off`/`internal` gateway the origin bridge doesn't apply.
+  `:443` host sites). On an `off` (plain-HTTP) gateway the origin bridge doesn't apply.
 - Cloudflare terminates TLS at the edge (it can see plaintext). For a
   no-third-party-in-path variant, the same `public: true` model can drive a
   self-hosted VPS + WireGuard edge instead — the toggle and generator stay; only the