optimize group based partitioner to not try to merge partitions we already determined were not supposed to be merged (#12798)

### Summary
In the group based partitioner we had a case where we would try to merge
partitions we already determined couldn't be merged, which was causing a
lot more checks to be done. This pr creates a set that tracks the
partitions that we determined cant be merged and ensures that when
considering 2 new partitions either id isnt in this set. Find below the
number of checks on whether each partition can be merged before and
after respectively which has a runtime of O(n^2) where n represents the
number of nodes in a partition.
<img width="84" height="772" alt="image"
src="https://github.com/user-attachments/assets/e1f7b47f-9006-494f-afe1-4da0726362f0"
/>

<img width="68" height="766" alt="image"
src="https://github.com/user-attachments/assets/45d4dbe0-f292-4f80-8e66-53aa68ef3cdb"
/>

### Test plan
I added cnt print logs to check to see the number of times we entered
the check both before and after the change.

Author: leafs1

exir/backend/canonical_partitioners/group_partitioner.py

@@ -204,35 +204,37 @@ def _merge_partitions(
         partitions_order,
     ):
         """Merge partitions when possible."""
-        merged = True
-        while merged:
-            merged = False
-            partition_ids = list(partitions_by_id.keys())
+        # Get current partition IDs
+        partition_ids = list(partitions_by_id.keys())
 
-            for i, p1 in enumerate(partition_ids):
-                if p1 not in partitions_by_id:
+        # Set to track removed partitions from initial static list so we can skip them
+        already_merged = set()
+
+        # Try to merge each pair of partitions
+        for i, p1 in enumerate(partition_ids):
+            # Skip if this partition has been already merged
+            if p1 in already_merged:
+                continue
+
+            for p2 in partition_ids[i + 1 :]:
+                # Skip if this partition has been already merged
+                if p2 in already_merged:
                     continue
 
-                for p2 in partition_ids[i + 1 :]:
-                    if p2 not in partitions_by_id:
-                        continue
-
-                    # Try to merge partitions if it doesn't create cycles
-                    if self._can_merge_partitions(p1, p2, partitions_by_id):
-                        self._perform_partition_merge(
-                            p1,
-                            p2,
-                            partitions_by_id,
-                            assignment,
-                            partition_users,
-                            partition_map,
-                            partitions_order,
-                        )
-                        merged = True
-                        break
-
-                if merged:
-                    break
+                # Try to merge partitions if it doesn't create cycles
+                if self._can_merge_partitions(p1, p2, partitions_by_id):
+                    self._perform_partition_merge(
+                        p1,
+                        p2,
+                        partitions_by_id,
+                        assignment,
+                        partition_users,
+                        partition_map,
+                        partitions_order,
+                    )
+
+                    # Mark p2 as merged
+                    already_merged.add(p2)
 
     def _perform_partition_merge(
         self,