Well, you don't know if they do, or if they were just capitalising the start of their sentence while not feeing that the word needs a capital letter in and of itself.
(But yeah, personally I would capitalised both counties regardless of spelling/which name used.)
Another country's official name in English is "Republic of Türkiye". Since 2022.
In both cases, that is what officials from the country expect the country to be called, when using the English language.
For instance here
https://www.un.org/en/about-us/member-states/germany
https://www.un.org/en/about-us/member-states/turkiye