I’ve ordered from the online store quite regularly, and it works.
Yes, if the couriers are unreliable in your area, sorting out the loss of a purchase delivery can be irritating.
Same for sorting out clue-constrained cellular carriers, if you happen to have one of those.
With a competent carrier, the setup when the new iPhone arrives is little more than placing the two iPhones adjacent, and selecting the content migration. No SIM swapping, no additional steps, with the contents transferred from the existing to the new wirelessly. All of which is well described in the setup doc that’s included with the new iPhone.
If your existing iPhone is not at 13.5.1, update that while you’re waiting for the new iPhone to arrive.
The one wrinkle I’ve met here—and I think Apple fixed it—is an existing iPhone running a newer iOS version than the new iPhone—this can happen when Apple releases an iOS update while the iPhone is in transit—and that involved setting up the new iPhone as a new iPhone, updating iOS, and then restoring the backup. That worked. Restoring a backup only works from a backup created on the same or an older iOS version, and not a restore from a newer to an older iOS. Again, I think Apple fixed this.
And set up a backup to a local Mac or Windows system, or up to iCloud if you use that. Local backups are usually faster, but both work.