The point is that in our modern Arabic we use tamanna تمنى for wish and desire, but apparently it has other meanings too which one must take into account.
According to tafsir ibn Kathir agrees with the translation of sahih international and gives some quotes which emphasize the story of gharaniq and the satanic verses.
Imam al-Qurtoby interpreted it (My translation own take it carefully):
قوله تعالى : ( تمنى ) أي قرأ وتلا
(tamanaa) means read and recite
و ألقى الشيطان في أمنيته أي قراءته وتلاوته
Satan threw into it [some misunderstanding]. [sahih international] means in his recitation or reading
he also quoted some ahadith about the revelation of the verse adding that none of them can be qualified as sahih (see the quote from a-Shifa).
he also quoted that amany أماني in 2:78 means recitations (as it is a plural) and in context can also mean lies instead of desires and wishes or what our nafs tells us. This may mean that the translation of sahih international here is wrong!
Sheikh a-Taher Benachour in his tahrir wa-tanwir left the gharaniq story aside and said: tamana here means wishes and desires as all the Messengers and Prophets wished guidance for their followers and nations while the shaitan/satan tries to misguide them by waswas ordering them to disbelieve, reject and disobey the orders of Allah. He also said after quoting a verse from a poem of Hasan ibn Thabit that he doesn't think that tamanna has the meaning to recite or more correctly that umniyah doesn't mean recitation:
تمنى كتاب الله أول ليله * تمني داود الزبور على مهل
فلا أظن أن القراءة يقال لها أمنية
Al-Qurtoby and in tafsir al-bahr al-moheet the same verse of the poem was used in the interpretation as a lingusitic proof of amany meaning recitations!
In al-bahr al-moheet the author added a meaning with a quote:
قال أبو مسلم : التمني نهاية التقدير ، ومنه المنية وفاة الإنسان للوقت الذي قدره الله
a-tamany is the end (time) of determination, as al-maniyah means the death of a human for the time Allah has determined.
Note that all Arabic dictionaries quote this verse (22:52)as an example for tamanna meaning to recite or read see for example here and here
In his a-Shifa al-Qadi 'Iyad said after quoting this verse and the story of gharaniq and explaining the infallibility of the Prophet (The pages I refer to are for the English part of my linked eBook):
... The proof are evident as for the miracle of the truthfulness of the Prophet's sayings, and the scholars of profound knowledge unanimously agreed that he was infallible and safeguarded against telling about the things in contrary of inaccurate way whether on purpose or out of forgetfulness or erring. ...
So, behold -may Allah honour you- that our echo reply to obscurity of that hadith ... is of two approaches: First: to deem it to be weak. Second: To deem it to be approved.
As for the first approach, it is sufficient for you that the aforementioned hadith is not reported by anyone of the trustworthy narrators nor narrated by anyone of the reliable transmitters with sound, connected chain of transmission. Yet, it as well as its like, appeals to the commentators and chroniclers who are fond of every eccentric thing, and those who read everything in the newspapers and approve it, whether it is right or bad.
... Abu Bakr al-Bazzar said: We don't know that hadith to be connected to the Prophet (pbuh) as for its narration with a connected transmission except in that way we mentioned. No one transmitted it on the authority of Shu'ba but Ummayya bin Khalid, and another one narrated it through the Mursal hadith, on the authority of Sa'id ibn Jubari. Yet, it is known through al-Kalbi through abu Saleh's authority on the authority of ibn 'Abbas. So, abu Bakr -may Allah have mercy upon him, illustrated to you that it is not known except in this way of transmission. According to what we have previously mentioned, that hadith is proven weak, doubtful, unreliable and devoid of the truth. As for the hadith related by al-Kalbi, it is not permitted to either narrate or state it due to being extremely weak and untrue as indicated by al-Bazzar -may Allah have mercy upon him. What is mentioned as for that hadith in as-Sahih is that the Prophet (pbuh) recited Surat, By the star while he was in Mecca and thereupon the Muslims the polytheists, the jinn and humans prostrated along with him. [594-595]
As you see most tafsir scholars quoted the meaning of tamanna = recite meanwhile they considered the story of the satanic verses as doubtful and weak. However ibn 'Achour said that this meaning appears to him wrong and he interpreted it desires and wishes.