docs(guide): name the project flag as load-bearing for build checks

CHANGELOG.md

@@ -18,6 +18,15 @@ aggregate instead: an italic *Catalog* line at the end of the version section an
 
 ### Fixed
 
+- **Deploy checks could report another project's builds** — the runbook's recipe for
+  "did this actually deploy?" flagged `--region` as the easy thing to forget and treated
+  `--project` as incidental. It is not. A gcloud install whose default project is a
+  different one returns *that* project's builds, and when its triggers happen to carry
+  the same names in the same region, the wrong answer is indistinguishable from the
+  right one — no error, just a credible list of `deploy-api` runs that stop a few days
+  ago. It produced a false "nothing has deployed since 2026-08-16" on a day with a dozen
+  deploys. `agentic/docs/project-guide.md` now names both flags and the context check
+  that settles it (#10484).
 - **The frontend deploy was broken by the version fix that preceded it** — #10485 read the version
   from the repo-root `pyproject.toml` at build time, but the frontend image is built with
   `docker build -f app/Dockerfile app`: the build context is `app/` alone, so nothing above it

agentic/docs/project-guide.md

@@ -898,7 +898,7 @@ Roughly five minutes from merge to live, per build.
 #### Checking whether something actually deployed
 
 The triggers are **regional, in `europe-west4`**, and regional builds do not
-appear in the global build list. Always pass `--region`:
+appear in the global build list. Always pass both `--region` and `--project`:
 
 ```bash
 gcloud builds list --region=europe-west4 --project=anyplot --limit=10 \
@@ -911,6 +911,17 @@ since — which reads as "nothing has deployed for months" and is simply the
 wrong list. That mistake has been made and had to be corrected by the repo
 owner.
 
+Omitting `--project` fails more quietly. A gcloud install whose default project
+is another one of the owner's projects returns *that* project's builds, and
+because those triggers carry the same names in the same region, the output looks
+entirely credible — a plausible list of `deploy-api` and `deploy-app` runs that
+simply stop a few days ago. There is no error to notice. Confirm the context
+before drawing a conclusion from it:
+
+```bash
+gcloud config get-value project    # must print: anyplot
+```
+
 `.github/workflows/notify-deployment.yml` only **records** a GitHub deployment;
 it does not deploy anything. A green run there says nothing about whether the
 code is live.