Could someone walk me through a transaction occurring on Ethereum involving danksharding and rollups?

I think I understand the classic idea of sharding relatively well. But I fail to really understand how "data sharding" works. Are the shards still actually blockchains? If they don't receive transactions are they updating their state or what is really happening? What data is stored where and when? Would really love to understand this finally.

Let me summarise my understanding of traditional sharding (including transactions) so that you can correct me on this in case I got even that wrong :).

The core idea of blockchains generally is that we want as many independent validators as possible so that they are incredibly unlikely to collude as they would need to collaborate to perform something in the direction of a 51% attack. So while we want as many different validators as possible we do not want them all to store all the data. We just want X amount of them to store the data to be sure that SOMEONE always has it. So basically everyone storing everything is simply an inefficient overkill of security because each validator that has the data makes it much less likely that all the data is lost. Instead, we could trade that inefficient security for scalability by having validators run subchains or shards. By doing so we run into two issues that we need to fix. 1) achieve shared security once again (prevent single shard takeover attack) 2) allow the shards to communicate so that the entire thing feels like one system again.

To do so we can shuffle the validators around which results in APPROXIMATELY the same game theoretic incentives as if the whole system was one Blockchain.

And we can allow the shard chains to prove to a chain maintained by everyone (the beacon chain) what their state is so that transactions on one shard chain can depend on that state. So that basically allows shards to communicate with each other.

But as I said before I have no clue how "data-sharding" really works.