feat(account): add eligible Intern picker query

docs/tests/integration/eligible-intern-picker.md

@@ -0,0 +1,97 @@
+# Test Evidence: Eligible Intern picker query
+
+- **Test type:** Integration
+- **Requirement IDs:** ACC-014, ACC-019–ACC-021, AUTH-001, PRJ-017, TST-001–TST-010
+- **Scenario IDs:** AC-ACC-009, AC-ACC-010, AC-PRJ-010 (selection-eligibility support)
+- **Test class/method:** com.lab.labtimesheet.feature.account.service.EligibleInternOptionIntegrationTest#listsOnlyActiveInternsWithActiveInclusiveInternshipsInPickerOrder
+- **Implementation commit:** Pending
+
+## Protected behavior
+
+Pending, locked, deactivated, non-Intern, not-started, completed, and date-expired records must not appear in the
+Account-owned Intern picker. An option is selectable only when both account and internship are ACTIVE and the
+explicit business date lies within the inclusive internship range. The returned numeric user ID is the internal
+submission identity, and options sort by display name then student code.
+
+## Test method
+
+The PostgreSQL 18.4 integration test persists valid account/profile combinations through the account feature's JPA
+entities and repositories. It uses SQL only as a test fixture for future lock, deactivation, and completion states
+whose production transitions are outside this change. It calls the public Account service query and compares the
+complete immutable DTO sequence, including both inclusive date boundaries and unique user IDs.
+
+## Hand-derived expected result
+
+For business date 2026-08-14, profiles starting on that date and ending on that date remain eligible. The only
+expected options are Alpha / STU-100, Alpha / STU-200, and Zeta / STU-300, in that order. Every other seeded
+row fails at least one account role/state, internship state, or inclusive date condition.
+
+## RED
+
+**Command**
+
+~~~text
+export JAVA_HOME=/opt/homebrew/opt/openjdk@25
+export PATH="$JAVA_HOME/bin:$PATH"
+export DOCKER_HOST=unix:///Users/sechmachine/.orbstack/run/docker.sock
+./mvnw -Dtest=EligibleInternOptionIntegrationTest test
+~~~
+
+**Observed result**
+
+~~~text
+[ERROR] EligibleInternOptionIntegrationTest.java:[11,54] cannot find symbol
+  symbol:   class EligibleInternOption
+  location: package com.lab.labtimesheet.feature.account.model.dto
+BUILD FAILURE
+~~~
+
+## GREEN
+
+**Command**
+
+~~~text
+export JAVA_HOME=/opt/homebrew/opt/openjdk@25
+export PATH="$JAVA_HOME/bin:$PATH"
+export DOCKER_HOST=unix:///Users/sechmachine/.orbstack/run/docker.sock
+./mvnw -Dtest=EligibleInternOptionIntegrationTest test
+~~~
+
+**Observed result**
+
+~~~text
+PostgreSQL 18.4 Testcontainers started and Flyway applied V1 baseline.
+Tests run: 1, Failures: 0, Errors: 0, Skipped: 0
+BUILD SUCCESS
+~~~
+
+## Affected suite
+
+**Command and result**
+
+~~~text
+export JAVA_HOME=/opt/homebrew/opt/openjdk@25
+export PATH="$JAVA_HOME/bin:$PATH"
+export DOCKER_HOST=unix:///Users/sechmachine/.orbstack/run/docker.sock
+./mvnw -Dtest=EligibleInternOptionIntegrationTest,AccountActivationIntegrationTest,BootstrapIntegrationTest,AccountWebIntegrationTest,AuthenticationWebIntegrationTest,BootstrapOnboardingWebIntegrationTest test
+
+Selected account reports: 13 tests, 0 failures, 0 errors, 0 skipped.
+
+./mvnw -Dtest=AccountActivationIntegrationTest test
+Tests run: 2, Failures: 0, Errors: 0, Skipped: 0
+BUILD SUCCESS
+
+./mvnw -Dtest=LayerStructureTest test
+Tests run: 1, Failures: 0, Errors: 0, Skipped: 0
+BUILD SUCCESS
+
+./mvnw test
+Tests run: 105, Failures: 0, Errors: 0, Skipped: 0
+BUILD SUCCESS
+~~~
+
+## External-test boundaries
+
+This query does not authorize Project membership itself; the consuming Project transaction must still recheck
+membership and ownership invariants. It does not test the later lifecycle mutation workflows that produce locked,
+deactivated, or completed rows.