My iPhone says Carrier Locked -> SIM Locked. How can I unlock this in order to use an eSIM?
Where did you buy this iPhone? If you are not in the US and/or bought the phone from a small vendor second hand, then you've been burned and need to get a refund from the seller.
In the US trading in my old iPhone and joining Verizon.
The device unlocking policy was changed last month to where you must pay off the device before it can be unlocked (or let your contract run its course, at which point it would be paid off from the monthly credits). Don't know if your current contract allows you to be grandfathered in on the old unlocking policy of "use for 60 days on Verizon". Your best bet would be to reach out to Verizon via one of their social media channels, as the CSRs aren't currently using these forums.