Will definitely try disconnecting the battery and see what happens.
It's difficult to describe but feels completely unnatural when it happens. I can understand when going even slightly uphill that the car will stay in a lower gear until either speeding up more or leveling out. Also sometimes when I lift and resume pressing the gas it resumes at the same gear.
I should probably take into the dealer as you guys suggested.
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Disconnecting the battery doesn't change the CVT's TCU (Transmission Control Unit). It resets the ECU (Engine Control Unit).
I'm convinced your expectations for your Impreza"s CVT are based on other transmissions and that what you have observed is, actually, normal behavior.
I've had 5 Subarus with a CVT so far, and ALL were different from any other transmission i've ever know... AND different behaviors from the different CVTs in all 5 cars. The Impreza having the most different of all. It doesn't behave like even I have come to know CVT behavior.
But after careful observation and analysis the Impreza's "puzzling" behavior is smart, being optimized to make the best use of its limited horselpower while always keeping fuel mileage as a priority. My advice is not to second guess what it's doing, although lifting briefly when you're close to a chosen speed then resuming at a stead, lower throttle level will enable the balance to shift to better gas milesge. If you want to see the specific 'gear' it's in, just flip the shift lever to Manual and the center display over the steering wheel will report the current gear. It won't change anything, but at least you can know more about which gear it's actually in.
Long story short, your dealership is going to advise you that your Impreza is working normally and that nothing's wrong. Having read your other posts it is clear you don't prefer owning the car. That bias is causing normal Impreza operations , though admittedly different from other vehicles, especially those which have formed your expectations, to appear ABnormal to you. Give it a little more time and appreciate what it CAN do for you. I've had a few SUVs (which you state you want) and anything with simiar performance and trim level will likely get worse fuel mileage and offer minimal storage advantages. If off-road is your thing, however, you can't beat an SUV... but it appears this is a commuter vehicle and IMO that's where it shines... given its amenities and overall highway performance.
I'm a little saddened to see a new owner unhappy with their Subaru, because I've been there. Those I only kept a year or less but waited until I was in a more advantaged place trade-in wise. Selling it outright right now is tough as Subaru is offering (still?) simply great deals and 0% interest rate on the '19s. That a big hurdle... IMO. YMMV