Can mongos 6.0 connect to mongodb 4.4?

In fact no, this is not the case. mongos need to be the same version as the mongod.

mongos can be a major version below the rest of the sharded cluster, during a version upgrade mongos is the last component to be upgraded before upgrading the FCV.

If you upgrade or use a mongos version higher than that of the cluster you’re likely to see mongos not connecting to the shard and config replica sets.

{
  "t": {
    "$date": "2022-11-05T18:20:19.555+00:00"
  },
  "s": "I",
  "c": "NETWORK",
  "id": 4712102,
  "ctx": "ReplicaSetMonitor-TaskExecutor",
  "msg": "Host failed in replica set",
  "attr": {
    "replicaSet": "c0",
    "host": "mongo-c-a:27019",
    "error": {
      "code": 188,
      "codeName": "IncompatibleServerVersion",
      "errmsg": "remote host has incompatible wire version: Server min and max wire version (9,9) is incompatible with client min wire version (13,13).You (client) are attempting to connect to a node (server) with a binary version with which you (client) no longer accept connections. Please upgrade the server’s binary version."
    },
    "action": {
      "dropConnections": false,
      "requestImmediateCheck": false,
      "outcome": {
        "host": "mongo-c-a:27019",
        "success": false,
        "errorMessage": "IncompatibleServerVersion: remote host has incompatible wire version: Server min and max wire version (9,9) is incompatible with client min wire version (13,13).You (client) are attempting to connect to a node (server) with a binary version with which you (client) no longer accept connections. Please upgrade the server’s binary version."
      }
    }
  }
}
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