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 Yunus 37:139-148 is very concise and it does not mention the length of time he spent inside the whale.
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.
Since it isn't possible to accurately answer this question from Islamic Tradition (God knows best), earlier revealed scripture should be consulted relying on Quran 10:94:
So if you are in doubt, [O Muhammad], about that which We have revealed to you, then ask those who have been reading the Scripture before you.
Verse Matthew 12:40 in the Enjeel answers this question concisely:
For as Jonah was three days and three nights in the belly of the whale, so will the Son of man be three days and three nights in the heart of the earth.