So, does this Verizon phone come locked?

Here is a screenshot of Verizon's Unlock Policy, for both prepaid and postpaid. Unfortunately, it does not mention 5G in particular, but it might be worth a call to their Support team to make sure it's the same.

PEW, your link appears to be the factory unlocked model.
The lower price listed is if you activate in-store on a new line on Verizon: you get a discount on the phone price for doing so.
This should not change the unlocked status of the phone, but you'll be paying for the first month's service on Verizon.

(That is a nice hefty discount.)