I want to ask does anybody know, How many days did Prophet Yunus / Jonah remained inside the whale until he was carried to the shore "according to the Quran"?
The Quranic story of Yunus37:139-148 is very concise and it does not mention the length of time he spent inside the whale.
From Tafsir Ibn Kathir:
واختلفوا في مقدار ما لبث في بطن الحوت، فقيل ثلاثة أيام، قاله قتادة. وقيل سبعة، قاله جعفر الصادق رضي الله عنه، وقيل أربعين يوماً، قاله أبو مالك. وقال مجاهد عن الشعبي التقمه ضحى، ولفظه عشية، والله تعالى أعلم بمقدار ذلك
They differed as to how long he spent in the belly of the fish. Some said three days; this was the view of Qatadah. Some said seven days; this was the view of Jafar As-Sadiq, may Allah be pleased with him. Some said forty days; this was the view of Abu Malik. Mujahid said, narrating from Ash-Sha`bi, "It swallowed him in the morning and cast him forth in the evening.'' And Allah knows best how long exactly was.
How many days did Jonah stay inside the whale? There are different narrations. From 9 hours, three days to forty days and this is not very clear. (1) According to some narrations, Yunus was in the whale's belly for 40 days and nights, during which time the whale did not eat so that Yunus would not be harmed. The fortieth day has come. Jonah prayed to God again, facing three kinds of darkness: night, sea, and fish belly. After this incident, God answered his prayer. (2) (2): Balami, History of Tabari, 1378, vol. 1, pp. 585-587.
(1)Ref:https://www.tasnimnews.com/fa/news/1395/10/06/1278987 (2): بلعمی، تاریخنامه طبری، ۱۳۷۸ش، ج۱، ص۵۸۵-۵۸۷.