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/tests/test_snapshot_compression.py

@@ -33,6 +33,7 @@ from sqlalchemy import text
 
 from app import compression, migrations, models
 from app.database import Base, SessionLocal, engine
+from tests import schema_rewind
 from tools.fakeprose import prose
 
 
@@ -196,8 +197,10 @@ def seed_pre_43(db, adventure, count: int = 4) -> dict[int, dict]:
 
     expected = {action_id: snapshot(action_id) for action_id in ids}
     as_json_column(db, expected)
-    db.execute(text(f"PRAGMA user_version = {migrations.SNAPSHOT_COMPRESS_VERSION - 1}"))
     db.commit()
+    # Take the later migrations' columns back off too, not just the stamp:
+    # replaying 43-45 also replays everything appended after them.
+    schema_rewind.rewind_to(engine, migrations.SNAPSHOT_COMPRESS_VERSION - 1)
     return expected