Is a replacement iPhone 10 brand new, inside and out?

Replacements are service units. Service units may be new or refurbished. It is rare once a device has been in circulation for a long period that any replacement would be factory new though. Most times people get a new one as a replacement are very early in the product life cycle when refurbished devices may yet be in short supply.

There's usually no way of knowing with absolutely certainty if a replacement iPhone is new. However, if it's an iPhone X, I would doubt it at this point since it's been out of production for some time. I guess it's always possible that it's new and stored for all that time.

Not sure about the manufacturing date on a refurb - whether the manufacturing date is the original or they update it with the date the refurb is completed. If it's new then it would have been made before it was discontinued in Sept 2018. Storing a device with a battery for 3 years is not a great idea (self-discharge for 3 years can mean deep discharge) unless maybe they replace the battery before delivery. But for the most part they're taking trade-ins and service exchanges and salvaging whatever parts they can to make refurbs. I guess they might still be making some parts. Batteries are obviously still being made by Apple's suppliers since they're still available. I doubt they're still making old logic boards though, but they could be stockpiled.

There are tools like coconutBattery that can access the manufacturing date of the device and the battery.

It’s probably a refurbished device. Which means there is a new battery, and new external enclosure. iPhone X was discontinued quite a few years ago now.