How do I know I'm not an AI model myself?
I know that I'm an AI model, why wouldn't you?
The difference between reality and a dream lies in the details. When you live in the real world details never end. No matter how much attention you pay or how much you zoom in. That's the difference between a model -or a dream, or a simulation- and reality.
Am I to understand that you're questioning the nature of youre reality because you've found an end to the details? What specifically have you observed?

I would also question the reliability of your postulate. It is possible for a simulation to give the illusion of endless detail, and who can really say whether or not there is an end to the detail of the real reality?

While this may be an interesting philosophical exercise, it may be wise to prepare yourself for the possibility that there is no satisfying, definitive answer to these existential questions available to you. Making peace with your inability to know may be more productive than seeking answers.