Make sqlite database migrations transactional again, part two (#14926)

#14910 fixed the regression introduced by #13873 where sqlite database
migrations would no longer run inside a transaction. However, it
committed the transaction before Synapse updated its bookkeeping of
which migrations have been run, which means that migrations may be run
again after they have completed successfully.

Leave the transaction open at the end of `executescript`, to restore the
old, correct behaviour. Also make the PostgreSQL behaviour consistent
with SQLite.

Fixes #14909.

Signed-off-by: Sean Quah <seanq@matrix.org>

synapse/storage/engines/sqlite.py

@@ -135,14 +135,16 @@ class Sqlite3Engine(BaseDatabaseEngine[sqlite3.Connection, sqlite3.Cursor]):
         > than one statement with it, it will raise a Warning. Use executescript() if
         > you want to execute multiple SQL statements with one call.
 
-        The script is wrapped in transaction control statemnets, since the docs for
+        The script is prefixed with a `BEGIN TRANSACTION`, since the docs for
         `executescript` warn:
 
         > If there is a pending transaction, an implicit COMMIT statement is executed
         > first. No other implicit transaction control is performed; any transaction
         > control must be added to sql_script.
         """
-        cursor.executescript(f"BEGIN TRANSACTION;\n{script}\nCOMMIT;")
+        # The implementation of `executescript` can be found at
+        # https://github.com/python/cpython/blob/3.11/Modules/_sqlite/cursor.c#L1035.
+        cursor.executescript(f"BEGIN TRANSACTION; {script}")
 
 
 # Following functions taken from: https://github.com/coleifer/peewee