[Synthetic _source] Deprecation and test upgrade to 9.x

[lucabelluccini]

Following #116689 we should test the following flow:

1. Create 8.latest cluster

2. Create an index where Synthetic _source is used

PUT demosourcesyn
{
  "mappings": {
    "_source": {
      "mode": "synthetic"
    }
  }
}

3. Index a document

POST demosourcesyn/_doc
{
  "field": "test"
}

4. Check the settings in GET demosourcesyn?include_defaults=true

5. Upgrade to 9.x

6. Index a document

POST demosourcesyn/_doc
{
  "field": "test2"
}

It must succeed

7. Check the settings in GET demosourcesyn?include_defaults=true

It must still index documents with Synthetic _source

[elasticsearchmachine]

Pinging @elastic/es-storage-engine (Team:StorageEngine)

[elasticsearchmachine]

Pinging @elastic/es-core-infra (Team:Core/Infra)