It appears the transaction with that id actually exists, you can verify it because Bitcoin transactions are public https://www.blockchain.com/btc/tx/1968cc2b31b396c3ef0677c69ed68a588f6bdec1ed9e60fcb8500fddda46b068. Indeed since it has ~900 confirmations, at an average block time of 10 minutes (Bitcoin protocol rules), it was first confirmed about a week ago.
The only explanations I can think of is related to the service and their application. If they do not choose to acknowledge the transaction or that it was sent to an address you own, that is between you and them.
from what I've heard from other users, this is a common problem caused by some delay in the blockchain (?) system
To answer this question, when you first submit a transaction to the Bitcoin network, the nodes will validate it, and if it passes, it will propagate throughout the nodes on the network. It is added to each node's mempool, which is where the transactions wait until a miner decides to add them to their block, and attempt to mine that block for a reward. When a miners decide to add your transaction to the next block is entirely up to them, but is generally dependent on the fee you decide to give them. The wallet software you used lets you select this fee, so the higher the fee the faster it will be mined (generally).
Another thing to understand is the application that is waiting for your transaction can decide how many blocks need to be mined after your transaction was submitted. This is known as confirmations. The reason for waiting more than 1 block is that if there is a conflict and 2 miners mine a block at the same time (unlikely), there is a reorganization of the blockchain, and your once confirmed transaction may become unconfirmed. So, it is a way to establish how permanent that transaction must be to be considered final. 6 is a typical minimum confirmation in Bitcoin, but can be higher or lower depending on the service or application. ~900 confirmations is much higher than usual and there should be no problem with confirmations with the service you used.