docs: document firebase scrypt password hash migration

docs/user-management/user-migration.mdx

@@ -104,6 +104,40 @@ The parameters are:
 }
 ```
 
+### Firebase scrypt support \{#firebase-scrypt-support}
+
+Logto also supports the [modified scrypt algorithm](https://github.com/firebase/scrypt) used by Firebase Authentication. Set `passwordAlgorithm` to `Legacy` and format the `passwordDigest` as follows:
+
+```json
+[
+  "firebase-scrypt",
+  ["salt", "signer_key", "salt_separator", "rounds", "mem_cost", "@"],
+  "expected_hashed_value"
+]
+```
+
+The parameters are:
+
+- **`salt`**: The user's `salt` from `firebase auth:export`
+- **`signer_key`**, **`salt_separator`**, **`rounds`**, **`mem_cost`**: Your project's password hash parameters, found in the Firebase console under **Authentication** > **Users** > **⋮** > **Password hash parameters**
+- **`@`**: Placeholder for the actual password value
+- **`expected_hashed_value`**: The user's `passwordHash` from the export, in standard base64. If you read users with the Firebase Admin SDK, convert its URL-safe base64 (`-`, `_`) to standard base64 (`+`, `/`) first.
+
+`passwordDigest` is limited to 256 characters, so serialize it as compact JSON without spaces (for example, with `JSON.stringify`).
+
+Users imported into Firebase with a non-scrypt hash who have not signed in since are exported with empty `passwordHash` and `salt`. Import them with their original hash if you still have it, or ask them to reset their password.
+
+**Example migration payload:**
+
+```json
+{
+  "username": "john_doe",
+  "primaryEmail": "john.doe@example.com",
+  "passwordAlgorithm": "Legacy",
+  "passwordDigest": "[\"firebase-scrypt\",[\"42xEC+ixf3L2lw==\",\"jxspr8Ki0RYycVU8zykbdLGjFQ3McFUH0uiiTvC8pVMXAn210wjLNmdZJzxUECKbm0QsEmYUSDzZvpjeJ9WmXA==\",\"Bw==\",\"8\",\"14\",\"@\"],\"lSrfV15cpx95/sZS2W9c9Kp6i/LVgQNDNC/qzrCnh1SAyZvqmZqAjTdn3aoItz+VHjoZilo78198JAdRuid5lQ==\"]"
+}
+```
+
 ## Steps to migrate \{#steps-to-migrate}
 
 1.  **Prepare the user data**