I'd get a Whitestone Dome Tempered Glass screen protector, regardless of any plastic screen protector, that may or may not be included.
I can confirm it does not. My S22 Ultra had a screen protector pre-installed. Saved me from having to spend $50 more for one from my local Best Buy. I received the S23 Ultra and it didn't so I haven't even used it in over a week. Tried to buy a screen protector but the store didn't have any, had to order one on Amazon and won't be here until next month.