My old SA at my local store used to overnight everything to me, even if it was just for one item less than that amount. I would do the payment link and it would show up at my door the next day- super convenient!! But my long distance SA seems to send most things (I feel like even if more than $6k) FedEx Ground as
@880 said… and it usually takes a day to tender it to FedEx and then 3-4 days to deliver. Shipments do arrive any day of the week, including Sundays. My DH worked it out with the FedEx delivery guy so now he leaves packages in a certain place so DH doesn’t have to go to the door to sign, since he’s in a lot of zoom meetings all day and got annoyed with all my deliveries.

If we’re away, I contact FedEx to put my deliveries on vacation hold.
Shipments from Paris seem to vary as well. Small items come via DHL directly and any issues I deal with DHL. This last shipment was a higher value shipment, and they used a third party vendor who coordinated shipping via FedEx. That was actually really great because I did have some issues with customs and the contact person at the shipping company helped me resolve them by liaising with Hermes and was in contact with me regularly about the status. I don’t know who I would’ve contacted at Hermes if they didn’t use this third party.