Thanks for asking this question... I was wondering if I didn't do a good job of describing how it is different from a traditional blockchain... but I wasn't sure.

Why can´t the centralized instance in the background collate those to also have the final sum you can work with?

https://dci.mit.edu/opencbdc

If you do a little bit of your own research you can see that what I'm saying is true and that even the MIT webpage admits it:

Privacy and Flexibility

Our design can support myriad access models without mandating specific policy choices. For example, our system could support, among other designs, models in which:

• Users fully self-custody their funds and receive payments without requiring an account with anyone (even the central transaction processor);

Key Concepts

• Decoupling transaction validation and execution

• Secure and flexible transaction formats

• Efficiency of transaction execution

Decoupling transaction validation and execution

This is the main difference that makes it so the money can't be accessed with a 12-word seed or normal private key. In order to have access to the money, the wallet needs to repopulate every single active transfer that was given to them. If you don't have this information you can't spend the money. You need the private key IN ADDITION to proof of the output transaction. This allows everything to be private and makes block explorers impossible. It would be impossible to see where money is going unless you directly controlled the nodes that run the system (and it has a fault tolerance of two nodes, so it sounds like it only has 3 nodes running total: by the same entity).

Blockchain addresses work that way too, if you look at a certain address (like e.g. @edicted is a wallet address) it shows the current amount of tokens at a glance.

No, because again, there are only 3 nodes, and those nodes do not have an API.
The CBDC nodes are 100% private and will not give information out to anyone.
It would be impossible to create a database that tells you which wallet has how much money inside.

Does this make sense?

I'm truly wondering if I'm explaining this correctly.
I understand it, but not well enough to explain it to others.