It is not cross-chain because here is a central point to pass through, so what you have done is the following:
- You deposited to a central platform.
- The data has been updated in that central platform.
- The withdrawal was made from the central platform to toher blockchain.
There is no cross-chain Bridge here as you can do it in one step if you use Automade CEXs.
The difference in using the central platform will not change anything.
Ideal cross-chain bridge is a bridge that connects several blockchains using smart contracts, something that has not been applied perfectly.
The best you will get is the decentralized swap exchange between tokens within the single blockchain.