fix: save Postgres state for apps without a partition key

[sangkyoonnam]

The Postgres persisters now save state when the application has no partition key. Today an app built without with_identifiers(partition_key=...) fails on its first step with either persister.

ApplicationBuilder leaves partition_key as None, and PostgreSQLPersister.save and AsyncPostgreSQLPersister.save pass it through as SQL NULL. partition_key is part of the primary key, so the insert fails. On main, an app with initialize_from(persister, ...) and with_state_persister(persister) and no partition key raises psycopg2.errors.NotNullViolation: null value in column "partition_key" on step(), and asyncpg.exceptions.NotNullViolationError on astep(). load already maps None to PARTITION_KEY_DEFAULT (""), and the SQLite persisters do the same in save, so this aligns save with both. Forking from such an app, or spawning MapStates sub-applications that inherit its None key, hit the same error and work with this change. I noted this in my #786 review, where the journal tables have the same issue.

Changes

• PostgreSQLPersister.save and AsyncPostgreSQLPersister.save map a None partition key to PARTITION_KEY_DEFAULT, the same way load does, and annotate it as Optional[str].

How I tested this

• Two new tests, one per persister, save and load with partition_key=None. Both fail on main with the not-null error and pass here.
• The Postgres tests ran against a local postgres:15 container with BURR_CI_INTEGRATION_TESTS=true: 13 passed. The app-level repro above steps without error on both persisters with this change.
• pytest tests --ignore=tests/integrations/persisters/test_postgresql.py --ignore=tests/integrations/test_bip0042_bedrock.py: 680 passed, 4 skipped.
• pre-commit run on the changed files passes.

Notes

• list_app_ids(None) on the Postgres persisters still matches nothing, while SQLite maps None to "" there too. fix: list each app once in SQL persister list_app_ids, newest save first #942 changes the same function, so I'll follow up once it lands rather than conflict with it.
• The existing Postgres tests always pass a partition key, which is why this didn't show up in CI.
• I wrote this with Claude Code and reviewed and ran it myself.

Checklist

• PR has an informative and human-readable title (this will be pulled into the release notes)
• Changes are limited to a single goal (no scope creep)
• Code passed the pre-commit check & code is left cleaner/nicer than when first encountered.
• Any change in functionality is tested
• New functions are documented (with a description, list of inputs, and expected output)
• Placeholder code is flagged / future TODOs are captured in comments
• Project documentation has been updated if adding/changing functionality.

[elijahbenizzy]

LGTM for save -- right layer is the persister, not the hook, since Mongo stores None literally and the save docstring leaves it to each backend. The list_app_ids half of the same gap lands via #950. Elijah