Give every action a branch and a depth

Phase 14 SP1. The tree goes into the schema and nothing reads it yet: a
`branches` table, `branch_id`/`depth` on actions and memories, a head pointer
on adventures, migrations 46-52, and a server-side backfill that re-reads every
existing adventure as a tree with one branch. `depth` holds the number `index`
already held, gaps included, so no story changes — a linear story *is* a tree
with one branch, which is what makes the SP0 baseline passing unmodified the
pass condition rather than a hope.

The writer had to come with it. No migration will ever visit a row written
after it ran, so columns backfilled today and populated next subphase would
leave a hole exactly the width of one deploy, and from SP2 on a row without a
branch is a row no read can see. `app/tree.py` owns that: one module, because a
node written without a branch fails by disappearing rather than by raising.

Three things the schema itself insisted on:

- `adventures.head_branch_id` is a plain integer, not a foreign key. Pointing
  both ways makes the two tables a cycle create_all cannot order, and its
  escape hatch needs an ALTER SQLite does not have. It is a cache, and a head
  naming a branch that is gone recovers onto the root.
- `lineage` is NOT NULL, so the backfill inserts `'[]'` and fills it in a
  second pass guarded on `json_array_length(lineage) = 0` — not `= '[]'`,
  because Postgres `json` has no equality operator.
- SQLite will not drop a column a foreign key names, which is how two existing
  tests broke: they simulated an old database by rewinding the stamp while
  leaving the new columns in place. Every ADD COLUMN migration is now
  idempotent, and `tests/test_tree_migration.py` builds a genuine schema 45 by
  rebuilding three tables from frozen DDL so the real ALTERs run.

297 tests green, 14 of them new. `branches` costs 0.1 kB of a 733.5 kB turn;
page load and index are byte-identical to the recorded figures.

The deploy that ships this needs one `VACUUM FULL actions;` on the direct
endpoint afterwards — it rewrites every row.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_017Dvvqn9ZDR4ixeFPHNbww7

backend/seed_demo.py

@@ -9,7 +9,7 @@ adventure and script-library copies belong to the local user (only relevant
 on single-user installs).
 """
 
-from app import auth, models, migrations
+from app import auth, models, migrations, tree
 from app.database import SessionLocal, engine
 
 # create_all + user_version stamp; plain create_all would leave a fresh DB at
@@ -250,7 +250,13 @@ try:
         db.add(models.StoryCard(adventure_id=adventure.id, **card))
     for position, s in enumerate(SCRIPTS):
         db.add(models.AdventureScript(adventure_id=adventure.id, position=position, **s))
-    db.add(models.Action(adventure_id=adventure.id, index=0, type="start", text=scenario.prompt))
+    opening = models.Action(
+        adventure_id=adventure.id, index=0, type="start", text=scenario.prompt
+    )
+    # Through the same door create_adventure uses, so the seeded adventure has a
+    # story tree like every other one.
+    tree.place_action(db, adventure, opening)
+    db.add(opening)
     db.commit()
 
     print(f"Scenario  id={scenario.id}: {scenario.title}")