I remember the term Eire being used in English, but Ngram confirms it is just a memory.
Its use grew explosively towards the end of the Irish Free State and then went into linear decline which, if extrapolated, should have hit zero before 2020. So we can safely say it is obsolete in English. And I think it was used for the Republic of Ireland, not Ireland as a whole. The use of the word Éire in Irish is discussed in detail on Wikipedia.
But as far as the use of the word in English is concerned, there are three issues.
The term is effectively obsolete as I demonstrate above.
This new use of an Irish word that developed with the Irish Free State was used specifically to refer to Saorstát Éireann which would naturally abbreviate to Éire in Irish (since Éireann is just the genitive of Éire). This was the 26 counties that later became the Republic of Ireland.
I am not aware that the term was ever used in 20th-century English to refer to 'Ireland' as a whole. This is complicated by the fact that the Irish government and many Irish people do not recognise the border. However, since the term Eire is only used in English by those who wish to emphasise the border, we can say that this specific term does only refer to the 26 counties.
Now we come to an important crossover between politics and linguistics. Irish is inherently political. It is used by people of one political persuasion and mocked by people of another. One of the main political parties in Northern Ireland has a name in Irish. The others wouldn't countenance the use of Irish.
But Gaelic is completely different. Gaelic is not associated with one religion or one political viewpoint. None of the political parties has a Gaelic background or a Gaelic name, but they all like to be seen to be supporting the language. In my experience Gaelic speakers studiously avoid any political terminology for Ireland. They will refer to 'Ireland' as an island without any reference to modern political boundaries. So whilst the English term Ireland is sometimes used to refer to the 26 counties, it would be most unusual for the Gaelic term to be used in this sense. That means we can be 100% certain that the Èirinn in this sentence refers to the island, and is therefore not the same as the obsolete English Eire.
Having just read the section of the above Wikipedia article on Éire as a state name I have realized that they use of the term is extemely offensive (which is not the same as actually offending Irish people, something that I do not know about). It says in the Irish constitution (both original 1937 and current versions) that
The name of the State is Éire, or, in the English language, Ireland.
The British government refused to accept this and contemptuously used the term Eire for some time. As far as I am concerned, if the Irish say the correct term in English is Ireland then the correct term in English is Ireland and that is the end of the matter. D
Thank you. I have updated my comment above in the light of your information. I have always considered the BBC's policy of deliberately leaving out accents (i.e. mis-spelling) to be offensive (especially on someone's name) and this is a rather good case in point. The BBC seems to have stopped enforcing this rule so rigorously which pleases me greatly and correct spellings are slowly creeping in. A search on the new Ngram (updated since my previous post) shows that Éire started to be used in British English in about 2000 and has now reached about half the now-minute figure for Eire.
But as I have said before, English speakers are exceptionally bad at distinguishing vowel length and will certainly pronounce Éire and Eire the same. The same as they pronounce bàta 'boat' and bata 'stick' the same. And Là na Sàbaid 'Sabath day, Saturday' and Là na Sabaid 'Fighting day'.
And from the point of view of the English, up until about 1999, I am not sure there was much semantic difference between Éire and Eire. D