Some index stats are reset when the index is moved to another node

[fdartayre]

Elasticsearch version (bin/elasticsearch --version): 7.14.1

Description of the problem including expected versus actual behavior:
The search and indexing metrics from index stats are reset when the index is moved to another node. This is unintuitive and can easily be misleading.

Steps to reproduce:

1. Create an index with 4 documents

PUT my_index
{
  "settings": { 
    "number_of_replicas": 1
  }
}

POST my_index/_bulk
{ "index": { "_id": 1 }}
{}
{ "index": { "_id": 2 }}
{}
{ "index": { "_id": 3 }}
{}
{ "index": { "_id": 4 }}
{}

2. The indexing count is incremented accordingly

GET _stats?filter_path=indices.my_index.*.indexing.index_total

{
  "indices" : {
    "my_index" : {
      "primaries" : {
        "indexing" : {
          "index_total" : 4
        }
      },
      "total" : {
        "indexing" : {
          "index_total" : 8
        }
      }
    }
  }
}

3. Move the primary to another node

GET _cat/shards/my_index?v

index    shard prirep state   docs store ip         node
my_index 0     p      STARTED    4 2.9kb 172.21.0.2 es3
my_index 0     r      STARTED    4 2.9kb 172.21.0.3 es1

POST /_cluster/reroute
{
  "commands": [
    {
      "move": {
        "index": "my_index", "shard": 0,
        "from_node": "es3", "to_node": "es2"
      }
    }
  ]
}

4. The indexing stats are reset for the primary shard

GET _stats?filter_path=indices.my_index.*.indexing.index_total

{
  "indices" : {
    "my_index" : {
      "primaries" : {
        "indexing" : {
          "index_total" : 0
        }
      },
      "total" : {
        "indexing" : {
          "index_total" : 4
        }
      }
    }
  }
}

[elasticmachine]

Pinging @elastic/es-data-management (Team:Data Management)