They can always generate a transaction (with TXID) without broadcasting it, and if it isn't broadcasted it will never be confirmed as it won't show up in the mempool which explains why you're not seeing it in any block explorer. It's not exactly a bad thing as it's a process when spending from a cold storage.

So assuming that coinapult isn't pulling an exit-scam. I'm thinking that your transaction is still in queue waiting to be broadcasted. Your biggest problem is reaching out to their support team 'cause it seems dead.

Wishing you luck! also if it isn't a bother, it would be great if you can give us updates.