Prevent duplicate relationships; harden tree render against bad graphs

Root cause of the blank Jung tree: a child double-linked to the same parent
(and, generally, any cycle) made family-chart recurse forever.

Backend (the real fix):
- create_relationship now rejects an equivalent existing edge → 409.
  parent_child is directional (parent→child); partnership/sibling match the
  pair in either order. So you can't link the same two people the same way
  twice. (GEDCOM import already deduped; manual creates didn't.)

Frontend (defense in depth so data can never blank the view):
- Tree view sanitizes the graph before rendering: dedupes parents/spouses,
  drops self-links, and greedily breaks ancestor cycles (a person can't be
  their own ancestor); children are derived from the kept edges. The render is
  wrapped in try/catch and shows a note instead of a blank canvas, telling you
  which conflicting links were skipped.
- Person page surfaces the 409 ("They're already linked that way.").

59 backend tests pass (incl. dup-rejection + reverse-parent-child allowed).

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

backend/tests/test_relationship_dedup.py

@@ -0,0 +1,65 @@
+"""Duplicate relationships are rejected (no double-linking)."""
+
+from tests.conftest import auth, register
+
+
+async def _setup(client, email):
+    h = auth(await register(client, email))
+    tid = (await client.post("/api/v1/trees", json={"name": "T"}, headers=h)).json()["id"]
+
+    async def person(given):
+        return (
+            await client.post(f"/api/v1/trees/{tid}/persons", json={"given": given}, headers=h)
+        ).json()["id"]
+
+    return h, tid, person
+
+
+async def test_duplicate_parent_child_rejected(client):
+    h, tid, person = await _setup(client, "dup-pc@example.com")
+    karl = await person("Karl")
+    kid = await person("Kid")
+    body = {"type": "parent_child", "person_from_id": karl, "person_to_id": kid}
+
+    first = await client.post(f"/api/v1/trees/{tid}/relationships", json=body, headers=h)
+    assert first.status_code == 201
+    dup = await client.post(f"/api/v1/trees/{tid}/relationships", json=body, headers=h)
+    assert dup.status_code == 409
+
+
+async def test_duplicate_partnership_either_direction_rejected(client):
+    h, tid, person = await _setup(client, "dup-sp@example.com")
+    a = await person("A")
+    b = await person("B")
+
+    first = await client.post(
+        f"/api/v1/trees/{tid}/relationships",
+        json={"type": "partnership", "person_from_id": a, "person_to_id": b},
+        headers=h,
+    )
+    assert first.status_code == 201
+    # Same couple, reversed order — still a duplicate.
+    dup = await client.post(
+        f"/api/v1/trees/{tid}/relationships",
+        json={"type": "partnership", "person_from_id": b, "person_to_id": a},
+        headers=h,
+    )
+    assert dup.status_code == 409
+
+
+async def test_reverse_parent_child_is_allowed(client):
+    """A->B as parent_child shouldn't block B->A (different meaning)."""
+    h, tid, person = await _setup(client, "dup-rev@example.com")
+    a = await person("A")
+    b = await person("B")
+    r1 = await client.post(
+        f"/api/v1/trees/{tid}/relationships",
+        json={"type": "parent_child", "person_from_id": a, "person_to_id": b},
+        headers=h,
+    )
+    r2 = await client.post(
+        f"/api/v1/trees/{tid}/relationships",
+        json={"type": "parent_child", "person_from_id": b, "person_to_id": a},
+        headers=h,
+    )
+    assert r1.status_code == 201 and r2.status_code == 201