I have had a N20 Ultra 5G from Samsung UK and from Samsung Hong Kong and both have had usb-c headphones included in the box.
Did you buy from the official Samsung UK shop i.e https://www.samsung.com/uk/
As said it was units in the States that didn't have them in the box but could then be requested to be sent separately if required as a customer services gestue.
Was the phone's retail box seal intact?
If so then I'd certainly contact Samsung and ask them for support.
There is no adapter dongle in the box to be able to use your own 3.5mm earphones unfortunately.
No Samsung wouldn't give out free Samsung Buds. They are expensive and only available free as a promotional item when an eligible phone is purchased or Pre Ordered.
They should be able to post out a set of usb-c wired earphones however.
Contact the Samsung Online Store customer services. The number and email address should be in the packaging sent with the phone. If you can't see them I can supply the information for you.
Current Phone ~
Samsung Note 20 Ultra 5G SM-N9860_256Gb SnapDragon 865+
Samsung One Ui 3.1/ Android 11.
@Sammy: If your Note 20 Ultra is over 30 days old, and past the returns period, then I recommend reaching out to our Help Desk via the link below, or on Facebook or Twitter, where an advisor will be able to look at your available warranty options. Please have your proof of purchase to hand, as this will be required to verify ownership and your existing warranty.