Yes, you are right. I agree with that. The additional thing is that the orderbook can be looked at like (similar, not exact) molecules of water. A single molecule of water is not wet. And a single molecule of water can't be modeled by fluid dynamics. You can think of the orders in the orderbook as molecules of water. When there is enough of those discrete orders and transactions then what "emerges" is something greater that the individual parts. At a certain volume or mass the molecules of water form drops of water and those form masses of water that can be modeled with fluid dynamics and treated continuously.
You do say this as well:
"A model can approximate it in a continuous way, sure, but an actual orderbook will always be discrete."
Which is the same as saying (I might be wrong though, and I am not "quoting" to indicate you said it):
"An actual orderbook is discrete AND can be modeled in a continuous way."
I think that means we agree and arrive at the same place even if I think it's due to emergence in the market system and you think it is just something that exists in that market system.