No, this specific engine doesn't have oil dilluion problem. The only engine that has oil dillution problems is the turbocharged 1.5L 4 cylinder. I would do normal maintenance like changing synthetic oil every 5,000 miles.

You dodged a bullet. That 2.0 liter engine doesn’t have those oil dilution issues like the 1.5t engines do. 

Oil dilution mostly affects the 1.5 Turbocharged GDI engine, you got lucky and bought one with the 2.0 Naturally Aspirated GDI engine, which (mostly) if free of oil dilution long as you change your oil every 5000 miles, w/ full synthetic OEM recommended in owners manual. 3k is too often IMO, maybe 4k if you want to be safe. 

The K20C2 engine is a 2.0L I4 naturally aspirated engine with port injection (this engine is NOT GDI), so is not susceptible to oil dilution like the 1.5L (and even some 2.0L) turbocharged GDI engines are.  In my book, that’s as good as it gets for a modern engine.  I’d still change the engine oil no more than every 5,000 miles or once a year (if you don’t drive much).

Also for your reading and knowledge:

https://tiremeetsroad.com/2021/03/17/heres-what-makes-the-honda-civic-base-2-0l-na-engine-the-civic-type-r-2-0l-turbo-engine-different/