We have lots of cold starts here in Colorado at 7,500ft. I don't recall our '23 Wildtrak ever having a late shift like you've described. Sure, in 'Sprot' and 'Baja' GOAT modes there are higher RPM shift points, but am assuming you're not in those modes..
FYI, I run a 15 count primer spin on our 2.7L before cold starts and don't back out until the warmup idle drops below 1,000 RPMs.
Suggest a dealership visit to check your tranny. I had our dealer check a engine surge issue we have with low range 4 mode down shifts. Heck, they kept our Bronco a week on that visit and said it was operating at factory spec..
Cheers