Definitely understand that concern - I've seen others post similar dealer responses here. My dealer did the battery swap rather than cable overlay replacement for some reason but they're gonna take care of the cable piece next week.
I'd definitely recommend contacting the dealership to look at it. I have a 2022 Lariat that went over a year of ownership before I started getting the deep sleep notifications. Took it in, they replaced the 12v battery and in the couple of months since then I've gotten the battery saver mode...
As one of the many 2022 model guinea pigs, I'm truly starting to mark the time for if/when they add AWD to the hybrid and I can go that route instead....
Yeah....looks like I'll be heading back to the dealer very soon because even after they replaced my battery last month I just got the battery saver mode again today. The curse of being a 2022 model guinea pig.... 😔