I picked up my '23 GT the week before you and it's due to go in for it's 600 mile service on Saturday. I found that after 150-200 miles the engine really seemed to loosen up well. I also noticed, similarly to you, that I'd have to give the gear shift an extra kick on occasion (even across the lower gears). However, this seems to have loosened up a lot as well now (currently 567 miles on the clock) and the bike is now running really smoothly. During run-in, I tend to kick the bike through all the gears and run the bike up and down through the revs in each gear (within the rev limit per mileage recommendations) to give the bike, engine and gear box a good work out, riding on all road types, including short stints on the motorway.
I also noticed for the first few hundred miles that my left foot was taking a bit of a pounding (I wear Dainese riding trainers) and thought at one stage that I'd have to buy some short leather boots with some good gear shift padding, but it all seems fine now so not an issue. I also thought it may just have been due to the fact that I wasn't used to riding foot-forward (my last bikes were a Speed Triple and a Bobber) so maybe I'm also just a bit more used to it now.
I'd suggest that you just keep riding as much as possible to run it in properly. If you still find there's a problem at 600miles, report it to your dealer. It may have been that they tightened the engine a little more than normal when they built our bikes (I assume they were manufactured around the same time).
Stay safe and enjoy the ride!
