You are missing your Database from the connection String:
{
"name": "CosmosConnection",
"type": "Microsoft.DataFactory/factories/linkedservices",
"properties": {
"annotations": [],
"type": "CosmosDb",
"typeProperties": {
"connectionString": "AccountEndpoint=https://xxxx-xxxx-xxxx-xxxx.documents.azure.com:443/;Database=core",
"accountKey": {
"type": "AzureKeyVaultSecret",
"store": {
"referenceName": "MainKeyVault",
"type": "LinkedServiceReference"
},
"secretName": "CosmosAccessKey"
}
}
}
}