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.
If they pre-generated the txid they shouldn't forward it to the user but actually leave the withdrawal status at pending or something.
I have never seen a service that I use forward me a txid that hasn't been broadcasted to the network. Makes little sense in my book. It only causes unnecessary confusion.
I am waiting about 2 weeks now and my BTC withdraw is still processing. And I can't find this transaction on blockchain.
It's definitely a shady practice in this case. The user is waiting for two weeks now with a "non" broadcasted txid reeks of scam. I hope I'm wrong and OP will be getting his money, but I don't have much faith in a good outcome unfortunately.