fix(auth)!: the recovery phrase is proved by a key of its own

A key proof was a signature by the account's signing key, which every
signed-in device keeps in its keyring: whoever could read one, with a
code from its authenticator, set a new password without the password or
the phrase (the second reading's H1). The phrase now proves itself with
an Ed25519 key derived from its bits alone (halkyon_keys'
recoveryProofKeysOf, KDF context hlkrprf1, a sibling of the recovery
key), whose public half every setup, new phrase and account reset sends
and the register keeps (account_password.recoveryProofKey); the device
derives the secret half only while the phrase is typed. An account
without one (none exist outside development) proves no phrase until it
sets a new one; decoys check against a decoy proof key alike.

Migration (module, Learn's and Todo's servers, Learn's device schema):
ALTER TABLE "account_password" ADD COLUMN "recoveryProofKey" bytea;
nullable, so rows made before keep working and no data is touched.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Signed-off-by: Tizian 「ティツィアーン」 <raisondetredev@pm.me>

apps/learn/halkyon_learn_server/migrations/20261020185750538-recovery-proof-key/migration.json

@@ -0,0 +1,33 @@
+{
+  "__className__": "serverpod.DatabaseMigration",
+  "actions": [
+    {
+      "__className__": "serverpod.DatabaseMigrationAction",
+      "type": "alterTable",
+      "alterTable": {
+        "__className__": "serverpod.TableMigration",
+        "name": "account_password",
+        "schema": "public",
+        "addColumns": [
+          {
+            "__className__": "serverpod.ColumnDefinition",
+            "name": "recoveryProofKey",
+            "fieldName": "recoveryProofKey",
+            "columnType": 5,
+            "isNullable": true,
+            "dartType": "dart:typed_data:ByteData?"
+          }
+        ],
+        "deleteColumns": [],
+        "modifyColumns": [],
+        "addIndexes": [],
+        "deleteIndexes": [],
+        "addForeignKeys": [],
+        "deleteForeignKeys": [],
+        "warnings": []
+      }
+    }
+  ],
+  "warnings": [],
+  "migrationApiVersion": 1
+}

apps/learn/halkyon_learn_server/migrations/20261020185750538-recovery-proof-key/migration.sql

@@ -0,0 +1,57 @@
+BEGIN;
+
+--
+-- ACTION ALTER TABLE
+--
+ALTER TABLE "account_password" ADD COLUMN "recoveryProofKey" bytea;
+
+--
+-- MIGRATION VERSION FOR halkyon_learn
+--
+INSERT INTO "serverpod_migrations" ("module", "version", "timestamp")
+    VALUES ('halkyon_learn', '20261020185750538-recovery-proof-key', now())
+    ON CONFLICT ("module")
+    DO UPDATE SET "version" = '20261020185750538-recovery-proof-key', "timestamp" = now();
+
+--
+-- MIGRATION VERSION FOR halkyon_base
+--
+INSERT INTO "serverpod_migrations" ("module", "version", "timestamp")
+    VALUES ('halkyon_base', '20261020185619505-recovery-proof-key', now())
+    ON CONFLICT ("module")
+    DO UPDATE SET "version" = '20261020185619505-recovery-proof-key', "timestamp" = now();
+
+--
+-- MIGRATION VERSION FOR serverpod
+--
+INSERT INTO "serverpod_migrations" ("module", "version", "timestamp")
+    VALUES ('serverpod', '20260824182259319', now())
+    ON CONFLICT ("module")
+    DO UPDATE SET "version" = '20260824182259319', "timestamp" = now();
+
+--
+-- MIGRATION VERSION FOR serverpod_auth_idp
+--
+INSERT INTO "serverpod_migrations" ("module", "version", "timestamp")
+    VALUES ('serverpod_auth_idp', '20260924105404509', now())
+    ON CONFLICT ("module")
+    DO UPDATE SET "version" = '20260924105404509', "timestamp" = now();
+
+--
+-- MIGRATION VERSION FOR serverpod_offline_sync
+--
+INSERT INTO "serverpod_migrations" ("module", "version", "timestamp")
+    VALUES ('serverpod_offline_sync', '20260914143806119', now())
+    ON CONFLICT ("module")
+    DO UPDATE SET "version" = '20260914143806119', "timestamp" = now();
+
+--
+-- MIGRATION VERSION FOR serverpod_auth_core
+--
+INSERT INTO "serverpod_migrations" ("module", "version", "timestamp")
+    VALUES ('serverpod_auth_core', '20260924105232991', now())
+    ON CONFLICT ("module")
+    DO UPDATE SET "version" = '20260924105232991', "timestamp" = now();
+
+
+COMMIT;

apps/learn/halkyon_learn_server/migrations/migration_registry.txt

@@ -37,3 +37,4 @@
 20261019204112282-deletion-notices
 20261020111943300-passwords
 20261020125117584-sessions-ended
+20261020185750538-recovery-proof-key