Delivery method do not applies on cart page

Not sure where is the problem. After i choice country and delivery method in cart page, press next and in billing page i get wrong country again. It looks in front end good country but after i scroll to the botton to check methods i see wrong methods for this country. If i click on billing country it shows different country selected in dropdown menu.

I have made screen record: https://youtu.be/gvX41dX5Wu8

I’m using latest version:
Woocommerce: Versija 4.5.1

Tried to downgrade to version 4.4.1 version. Situation the same.

Changed theme and disabled all custom code problem remained the same.

The page I need help with: [log in to see the link]