Actually , no, you're focusing on the wrong word which you think is a key word.
The keyword is actually "United" and this tells us that Great Britain and Northern Ireland are united as one sovereign country. Hence, Northern Ireland isn't separate from Great Britain which the Belfast Agreement explicitly acknowledged. It's an INTEGRAL part of the United Kingdom until or unless we in Northern Ireland decide to leave the Union.
In the context of the full name of the United Kingdom of Great Britain and Northern Ireland, the term "and" does not itself imply separation:
"And" - "used to connect words of the same part of speech, clauses, or sentences, that are to be taken jointly."
This doesn't imply separation. It implies unity of the two into one.
You have to bear in mind that for most of human history the sea was NOT a "natural barrier" and didn't itself suggest a separation of places. This concept still survives in the 21st Century in places such as the USA, Portugal, Spain, Indonesia, etc as well as within the United Kingdom.
In contrast, the word "and" in this sentence "Northern Ireland and the Republic of Ireland" implies there is NOT one Ireland....but two. In that context, it spells out separation which is also the corresponding reality.