fix: Follow up metrics fixes vol.2 (matter-labs#656)

## What ❔

Fix oldest not generated batch query

## Why ❔

For metrics to work correctly

## Checklist

- [x] PR title corresponds to the body of PR (we generate changelog
entries from PRs).
- [ ] Tests for the changes have been added / updated.
- [ ] Documentation comments have been added / updated.
- [x] Code has been formatted via `zk fmt` and `zk lint`.
- [x] Spellcheck has been run via `cargo spellcheck
--cfg=./spellcheck/era.cfg --code 1`.

core/lib/dal/sqlx-data.json

@@ -2717,24 +2717,6 @@
     },
     "query": "UPDATE transactions\n                SET in_mempool = TRUE\n                FROM (\n                    SELECT hash FROM (\n                        SELECT hash\n                        FROM transactions\n                        WHERE miniblock_number IS NULL AND in_mempool = FALSE AND error IS NULL\n                            AND (is_priority = TRUE OR (max_fee_per_gas >= $2 and gas_per_pubdata_limit >= $3))\n                            AND tx_format != $4\n                        ORDER BY is_priority DESC, priority_op_id, received_at\n                        LIMIT $1\n                    ) as subquery1\n                    ORDER BY hash\n                ) as subquery2\n                WHERE transactions.hash = subquery2.hash\n                RETURNING transactions.*"
   },
-  "2cc57497090a97bcb453036f7b5e2139b590699aa1a2df4d6fd2b19e27e06251": {
-    "describe": {
-      "columns": [
-        {
-          "name": "l1_batch_number",
-          "ordinal": 0,
-          "type_info": "Int8"
-        }
-      ],
-      "nullable": [
-        false
-      ],
-      "parameters": {
-        "Left": []
-      }
-    },
-    "query": "SELECT l1_batch_number FROM proof_generation_details WHERE status <> 'generated' ORDER BY l1_batch_number ASC LIMIT 1"
-  },
   "2e3f116ca05ae70b7c83ac550302194c91f57b69902ff8e42140fde732ae5e6a": {
     "describe": {
       "columns": [],
@@ -4853,6 +4835,24 @@
     },
     "query": "SELECT (SELECT l1_batch_number FROM miniblocks WHERE number = $1) as \"block_batch?\", (SELECT MAX(number) + 1 FROM l1_batches) as \"max_batch?\""
   },
+  "5f29e71af038c974e2d83b908c5a2559ab8afbb169bc0ae9f881a6628dc087fd": {
+    "describe": {
+      "columns": [
+        {
+          "name": "l1_batch_number",
+          "ordinal": 0,
+          "type_info": "Int8"
+        }
+      ],
+      "nullable": [
+        false
+      ],
+      "parameters": {
+        "Left": []
+      }
+    },
+    "query": "SELECT l1_batch_number FROM proof_generation_details WHERE status NOT IN ('generated', 'skipped') ORDER BY l1_batch_number ASC LIMIT 1"
+  },
   "5f40849646bb7436e29cda8fb87fece2a4dcb580644f45ecb82388dece04f222": {
     "describe": {
       "columns": [

core/lib/dal/src/proof_generation_dal.rs

@@ -109,7 +109,7 @@ impl ProofGenerationDal<'_, '_> {
         .ok_or(sqlx::Error::RowNotFound)
     }
 
-    pub async fn get_oldest_unprocessed_batch(&mut self) -> Option<L1BatchNumber> {
+    pub async fn get_oldest_unpicked_batch(&mut self) -> Option<L1BatchNumber> {
         let result: Option<L1BatchNumber> = sqlx::query!(
             "SELECT l1_batch_number \
              FROM proof_generation_details \
@@ -129,7 +129,7 @@ impl ProofGenerationDal<'_, '_> {
         let result: Option<L1BatchNumber> = sqlx::query!(
             "SELECT l1_batch_number \
              FROM proof_generation_details \
-             WHERE status <> 'generated' \
+             WHERE status NOT IN ('generated', 'skipped') \
              ORDER BY l1_batch_number ASC \
              LIMIT 1",
         )

core/lib/zksync_core/src/house_keeper/fri_prover_queue_monitor.rs

@@ -92,13 +92,10 @@ impl PeriodicJob for FriProverStatsReporter {
 
         if let Some(l1_batch_number) = db_conn
             .proof_generation_dal()
-            .get_oldest_unprocessed_batch()
+            .get_oldest_unpicked_batch()
             .await
         {
-            metrics::gauge!(
-                "fri_prover.oldest_unprocessed_batch",
-                l1_batch_number.0 as f64
-            )
+            metrics::gauge!("fri_prover.oldest_unpicked_batch", l1_batch_number.0 as f64)
         }
 
         if let Some(l1_batch_number) = db_conn