Make the shipped example envs ones that can actually start

The krow-2 deploy failed on the ANTHROPIC_API_KEY guard, which is the guard
doing its job. Checking what an operator hits *after* fixing it turned up two
older faults in the files they are told to copy — both predating the Groq
switch, both fatal at boot.

HTTP_WRITE_TIMEOUT shipped as 30s in .env.example, .env.docker.example and the
compose default, while validateWriteTimeout refuses anything at or under the
deep tier's 2m deadline. `cp .env.docker.example .env && docker compose up`
could not start. Now 180s. krow-2 never saw this because someone had already
overridden it in that environment.

.env.docker.example carried no model block at all, so a production stack built
from it is refused for a missing MODEL_API_KEY. Added, with the Groq defaults
and the reasoning-effort note (most non-reasoning models reject the request
rather than ignoring the key).

Neither was subtle. Both survived because the examples were prose to every test
in this package: the validator and the file documenting it had no mechanical
connection, so tightening one silently invalidated the other. That connection
is now TestShippedExampleEnvActuallyBoots, which parses each example and runs
Load() on it under the APP_ENV the file itself declares — production for the
docker one, development for the root one, each internally consistent. Verified
by mutation: reverting the timeout, removing the key line, and restoring a
claude-* id each fail it with the message an operator would see.

Go does not treat these files as test inputs, so an example-only edit can be
served a stale pass from the test cache. Noted in the test; use -count=1.

Also documented the upgrade path in handover.md, including the one thing
startup validation cannot catch: renaming ANTHROPIC_API_KEY to MODEL_API_KEY
without replacing the value boots fine and 401s on every run.

gofmt clean, go vet clean, 15/15 packages pass.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01PJvibeSc1JYXjatankqM1g

.env.example

@@ -16,7 +16,12 @@ LOG_LEVEL=info               # debug | info | warn | error
 HTTP_HOST=127.0.0.1
 HTTP_PORT=8080
 HTTP_READ_TIMEOUT=15s
-HTTP_WRITE_TIMEOUT=30s
+# 180s, not 30s. internal/config REFUSES TO START when this is below the deep
+# tier's 2m agent deadline: the server would abort the response mid-run and the
+# caller would see 502 from the proxy in front, a gateway error for something no
+# gateway did. 30s shipped here for a long time and was the cause of exactly
+# that incident. Anything at or under 2m0s is a container that will not boot.
+HTTP_WRITE_TIMEOUT=180s
 HTTP_IDLE_TIMEOUT=60s
 HTTP_SHUTDOWN_TIMEOUT=10s
 # Browser origins allowed to call this API cross-origin, comma-separated.