Assistance understanding this hadith about ʿUmar and the Prophet’s wives (sallallāhu ʿalayhi wa sallam)

As-salāmu ʿalaykum - I’m trying to get a clearer picture of this hadith from Ṣaḥīḥ al-Bukhārī (about ʿUmar ibn al-Khaṭṭāb رضي الله عنه and the revelation of the verses on hijab and the later verse 66:5). A few points I’m struggling with and would appreciate straightforward explanations or pointers to reliable tafsīr: 1) Why did ʿUmar (RA) ask the Prophet (صلى الله عليه وسلم) to have his wives cover up? The tafsīr I read says ʿUmar asked several times and the last time was after he saw Ṣaʿdah bint Zamʿa relieving herself at night and recognized her. Some sources imply ʿUmar was angry and pressed the issue. Why would he feel the need to push the Prophet (PBUH) on this? Wouldn’t the Prophet have implemented hijab for his household if he considered it necessary? 2) The hadith says ʿUmar learned the Prophet had blamed some of his wives, and so ʿUmar admonished them, even saying “either stop troubling the Prophet or Allah will give him better wives than you.” Why would ʿUmar intervene like that? Why would the Prophet complain about his wives to others, and if he wanted to advise them wouldn’t he do it himself? The wording of ʿUmar’s reproach feels a bit harsh or disrespectful to me - was that acceptable conduct toward the Prophet’s wives? 3) One of the wives replied to ʿUmar, asking whether the Prophet didn’t have the ability to advise his own wives, and then Quran 66:5 was revealed. It seems striking that that verse would come in response to ʿUmar’s words. Is the sequence here correctly understood? Why did the revelation occur in this context, and does this mean ʿUmar’s words caused that verse? I want a simple, balanced explanation that draws on classical tafsīr but stays easy to follow. If you can point to trustworthy commentaries (Ibn Kathīr, al-Ṭabarī, al-Baghawī, etc.) or explain how scholars reconcile the Prophet’s private role as advisor with ʿUmar’s public admonition, that would be helpful. JazakAllāhu khayran for any clarity or references.