What's the Sunni take on/perspective on incident of Hazrat Umar and bibi Fatima when he charged her during her pregnancy?
Sunnis consider the "incident" to be fabricated with the intention to slander Abu Bakr and Umar.
In Shia books which claim this incident, it is not recorded with a sound chain of narrators, so Sunnis do not accept it.
The oldest reference to this incident is the Shia book called Al-Saqifa (السقيفة) or Kitab Sulaym bin Qais ( كتاب سليم بن قيس ) which is a collection of narrations attributed to Sulaym bin Qays (سليم بن قيس الهلالي) and collected by Aban ibn abi-Ayyash (أبان بن أبي عياش فيروز) who is weak (ضعيف) and his book is fabricated (موضوع) according to Sunnis and also several Shia works on Ilm al Rijal such كتاب الرجال of ابن داوود الحلي :
٢ ـ أبان بن أبي عياش ، بالياء المثناة تحت والشين المعجمة فيروزين ( جخ غض ) ضعيف ، قيل إنه وضع كتاب سليم بن قيس
٢٢٦ ـ سليم بن قيس الهلالي ى ، ن ، سين ، ين ( جخ ) ينسب إليه الكتاب المشهور وهو موضوع بدليل أنه قال : إن محمد بن أبي بكر وعظ أباه عند موته. وقال فيه : إن الائمة ثلاثة عشر مع زيد. وأسانيده مختلفة ( غض ) : لم يرو عنه إلا أبان بن أبي عياش وفي الكتاب مناكير مشتهرة ، وما أظنه إلا موضوعا
Sunnis believe that this is a lie spun to degrade the Ahle Bait and to malign the Sahaba.
Ali, the Lion of Allah, whose bravery and strength is unmatched, would never have let such a thing happen on his watch. And if it had happened, Ali would never have pledged allegiance to Abu Bakr and Umar, and he would have taken swift revenge from them.
Instead Ali gave allegiance to both, and he said the following about Umar on his deathbed:
Narrated Ibn Abbas:
When (the dead body of) Umar was put on his deathbed, the people gathered around him and invoked (Allah) and prayed for him before the body was taken away, and I was amongst them. Suddenly I felt somebody taking hold of my shoulder and found out that he was Ali bin Abi Talib.
Ali invoked Allah's Mercy for Umar and said, "O Umar! You have not left behind you a person whose deeds I like to imitate and meet Allah with more than I like your deeds. By Allah! I always thought that Allah would keep you with your two companions, for very often I used to hear the Prophet (ﷺ) saying, 'I, Abu Bakr and Umar went (somewhere); I, Abu Bakr and Umar entered (somewhere); and I, Abu Bakr and Umar went out."'