Add a real live Linear/Codex E2E target

#### Context

Add a real end-to-end path for Symphony Elixir that exercises Linear and
Codex together, and make it easy to invoke explicitly from one Make target.

#### TL;DR

*Add a real live Linear/Codex E2E test plus a `make e2e` entrypoint.*

#### Summary

- Add an opt-in live Elixir test that creates a real Linear project and issue.
- Run a real Codex turn and verify both workspace output and Linear side effects.
- Require Codex to post a Linear comment and close the issue before completion.
- Add `make e2e` with clear failures for missing `LINEAR_API_KEY` or `codex`.
- Document the new E2E entrypoint and behavior in the Elixir README.

#### Alternatives

- Keep using ad hoc `mix test` commands and environment toggles.
- Keep shimming Linear or post-processing issue state locally.
- Those keep the happy path less reproducible and do not prove Codex can
  mutate Linear itself during the turn.

#### Test Plan

- [x] `make -C elixir all`
- [x] `env -u LINEAR_API_KEY make -C elixir e2e`
- [x] `LINEAR_API_KEY=$(tr -d '\r\n' < ~/.linear_api_key) SYMPHONY_RUN_LIVE_E2E=1 mix test test/symphony_elixir/live_e2e_test.exs`

Author: frantic-openai

elixir/Makefile

@@ -1,9 +1,9 @@
-.PHONY: help all setup deps build fmt fmt-check lint test coverage ci dialyzer
+.PHONY: help all setup deps build fmt fmt-check lint test coverage ci dialyzer e2e
 
 MIX ?= mix
 
 help:
-	@echo "Targets: setup, deps, fmt, fmt-check, lint, test, coverage, dialyzer, ci"
+	@echo "Targets: setup, deps, fmt, fmt-check, lint, test, coverage, dialyzer, e2e, ci"
 
 setup:
 	$(MIX) setup
@@ -33,6 +33,19 @@ dialyzer:
 	$(MIX) deps.get
 	$(MIX) dialyzer --format short
 
+e2e:
+	@if [ -z "$$LINEAR_API_KEY" ]; then \
+		echo "LINEAR_API_KEY is required for \`make e2e\`."; \
+		echo "Export it first, for example:"; \
+		echo "  export LINEAR_API_KEY=\$$(tr -d '\\r\\n' < ~/.linear_api_key)"; \
+		exit 1; \
+	fi
+	@if ! command -v codex >/dev/null 2>&1; then \
+		echo "\`codex\` must be on PATH for \`make e2e\`."; \
+		exit 1; \
+	fi
+	SYMPHONY_RUN_LIVE_E2E=1 $(MIX) test test/symphony_elixir/live_e2e_test.exs
+
 ci:
 	$(MAKE) setup
 	$(MAKE) build

elixir/README.md

@@ -173,6 +173,25 @@ The observability UI now runs on a minimal Phoenix stack:
 make all
 ```
 
+Run the real external end-to-end test only when you want Symphony to create disposable Linear
+resources and launch a real `codex app-server` session:
+
+```bash
+cd elixir
+export LINEAR_API_KEY=...
+make e2e
+```
+
+Optional environment variables:
+
+- `SYMPHONY_LIVE_LINEAR_TEAM_KEY` defaults to `SYME2E`
+- `SYMPHONY_LIVE_CODEX_COMMAND` defaults to `codex app-server`
+
+The live test creates a temporary Linear project and issue, writes a temporary `WORKFLOW.md`,
+runs a real agent turn, verifies the workspace side effect, requires Codex to comment on and close
+the Linear issue, then marks the project completed so the run remains visible in Linear.
+`make e2e` fails fast with a clear error if `LINEAR_API_KEY` is unset.
+
 ## FAQ
 
 ### Why Elixir?