You may read in imam Maliks al Muwatta' the following:
Yahya related to me from Malik that Yazid ibn Ruman said, "The people used to watch the night in prayer during Ramadan for twenty- three rakas in the time of Umar ibn al-Khattab."
In combination with the version of al-Muwatta', which was narrated by Yahya ibn Yahya al-Laithi saying:
Yahya related to me from Malik from Muhammad ibn Yusuf that as- Sa'ib ibn Yazid said, "Umar ibn al-Khattab ordered Ubayy ibn Kab and Tamim ad-Dari to watch the night in prayer with the people for eleven rakas. The reciter of the Qur'an would recite the Mi'in (a group of medium-sized suras) until we would be leaning on our staffs from having stood so long in prayer. And we would not leave until the approach of dawn."
We may conclude that the 23 from the first hadith must be understood as 20 raka'a + 3 raka'a witr.
Even if imam Malik reported the practice of the people of Medina as 36 + 3 raka'a witr or 38 + 1 raka'a witr, for himself he has chosen eleven raka'as.
Further even if Muhammad ibn Yusuf (al-'Araj) is trustworthy ibn 'Abd al-Barr commented this hadith saying that except with Malik it was narrated that the amount was twenty one not eleven raka's. However az-Zurqani disagreed because Sa'id ibn Mansur reportet the same and so did many other scholars. Ibn 'Abd al-Barr further assumed that it is possible that he ('Umar) started with eleven and moved to twenty one (this was also a position of al-Bayhaqi), another possibility is that the amount counts for men who were lead by Ubay and and the same amount for the women as he assumed that women and men didn't pray at the same time as assumed by ibn Hajar. Al-Mubarakpuri when discussing the hadith (version of imam at-Tirmdihi -see here-) showing that the prophet () himself lead a night prayer in Ramadan for 3 non consecutive days however insisted on the fact that the night prayer in Ramdan as performed by the prophet () and as initiated by 'Umar, was of 8 raka'a plus 3 raka'a of taraweeh. So al-Mubarakpuri and before him ibn Hajar showed that the statement of ibn 'Abd al-Barr that Malik might have been the only person reporting the amount of eleven raka'a from ibn Yusuf, was a mistake can be rejceted as a mistake of ibn A'bd al-Barr himself, because it has support in 2 more sources at least beside the fact that 'Aishah () stated that the night prayer of the prophet () was always the same eleven raka'a including the witr, or thirteen including fajr sunnah or 9 excluding two raka'a sunnah after 'Isha', it never changed be it in Ramdan or any other month of the year.
Many people claim that the majority of scholars say that taraweeh must be performed in congregation, however in his commentary of this hadith at-Tirmdidhi also mentioned the choices of the scholars, saying:
According at-Tirmdihi, among those who have chosen to pray in congregation are imam Ahamad, ibn al-Mubarak and Ishaaq (ibn Rahawayh?) while imam a-Shafi'i prefered to pray alone at home if one can recite and memorized at least some of the qur'an.
Imam at-Trimdihi commented the hadith saying that taraweeh was performed as follows:
41 rak'a including witr in Medina.
And the 20 which were reported on as the practice of the sahabah like 'Umar () and 'Ali ibn abi Talib ().
While imam Ahamad didn't make any choice saying that different amounts where mentioned o the topic.
Further the second narration confirms the typical recommendation for the night prayer or the sunnah/nafl after 'Isha' (see for example in al-Muwatta'). As a matter of fact none rejects this 8 raka'a + 3 raka'a option. But in the recommendations of madhhabs you may rather find:
20 Raka'as + witr
even 36 raka's + witr.
Imam al-Bayhaqi quoted the above hadith in his as-Sunan al-Kubra (see -here-) commenting with the addition:
Here and in the following I'm translating from Arabic language, as these translations are of my own take them carefully.
هَكَذَا فِي هَذِهِ الرِّوَايَةِ
it was narrated this way in this version (riwayah)
Then he mentioned a second narration (I'll add a short qualification of the narrators in my translation):
4288 - وَقَدْ أَخْبَرَنَا أَبُو عَبْدِ اللهِ الْحُسَيْنُ بْنُ مُحَمَّدِ بْنِ الْحُسَيْنِ بْنِ فَنْجَوَيْهِ الدَّيْنَوَرِيُّ بِالدَّامَغَانِ، ثنا أَحْمَدُ بْنُ مُحَمَّدِ بْنِ إِسْحَاقَ السُّنِّيُّ، أنبأ عَبْدُ اللهِ بْنُ مُحَمَّدِ بْنِ عَبْدِ الْعَزِيزِ الْبَغَوِيُّ، ثنا عَلِيُّ بْنُ الْجَعْدِ، أنبأ ابْنُ أَبِي ذِئْبٍ، عَنْ يَزِيدَ بْنِ خُصَيْفَةَ، عَنِ السَّائِبِ بْنِ يَزِيدَ قَالَ:
We were informed by abu Abdillah al-Hussayn ibn Muhammad inm al-Hussayn ibn Fanjawayh a-Dynoori (trustworthy died 414 a.H.) at a-Damghan, from Ahmad ibn Muhammad ibn Ishaaq (ibn) as-Sunni (trustworthy died 364 a.H.), from 'Abdullah ibn Muhammad ibn 'Abdal'aziz al-Baghawi (trusworthy 214-317 a.H.), from 'Ali ibn al-Ja'ad (trustworthy 136 - 230 a.H.) from ibn abi Di'b 82 -159 a.H.) from Yazid ibn Khosayfah (trustworthy among the teachers of imam Malik) from as-Sa'ib ibn Yazid (from among the young sahabah 3-91 a.H.) who said:
" كَانُوا يَقُومُونَ عَلَى عَهْدِ عُمَرَ بْنِ الْخَطَّابِ رَضِيَ اللهُ عَنْهُ فِي شَهْرِ رَمَضَانَ بِعِشْرِينَ رَكْعَةً " قَالَ: " وَكَانُوا يَقْرَءُونَ بِالْمَئِينِ، وَكَانُوا يَتَوَكَّئُونَ عَلَى عِصِيِّهِمْ فِي عَهْدِ عُثْمَانَ بْنِ عَفَّانَ رَضِيَ اللهُ عَنْهُ مِنْ شِدَّةِ الْقِيَامِ "
During the era of Omar Ibn al-Khattab, may Allah be pleased with him, in the month of Ramadan, they used to pray twenty rak’ahs.” He said: “And they used to recite the mi'in, and they would lean on their sticks during the era of Uthman ibn 'Affan, may Allah be pleased with him, because of the intensity of standing.
So as you may see the narrator chain of al-Bayhaqi is also strong and trustworthy.
So basically there's no opposition against the 20 raka'a taraweeh.
Is the amount really important?
I think before saying 'Umar has ordered people to pray 11 raka'a or 'Umar ordered to pray 20 raka'a we must know that first of all what was the sunnah of the prophet() and the Sahih hadith reported in al-Muwatta', and the Sahih books say that it was 11 raka'a and 'Aishah who know and observed and lived with the prophet () added her own comment saying to the son of 'Abdurrahman ibn 'Awf (who asked her):
... He prayed four - do not ask me about their beauty or length. Then he prayed another four - do not ask me about their beauty and length. Then he prayed three.
So the question was asked at the time of Sahabah abu Salamah ibn 'Abd ar-Rahman ibn 'Awf lived from 22 a.H. to 94 a.H. so the question was asked after the death of abu Bakr (who died 23 a.H.) and before 58 a.H. (as 'Aishah died this year) one coudl imagine that abu Salamah witnessed the change from 11 to 20 raka'a + witr and wanted to know the original case.
Further 'Aishah stated.
do not ask me about their beauty or length
Because the imam used to recite long surahs or stand a long time in recitation as you may read in the 2nd hadith above, this was at the time of 'Umar and later also in the era of 'Uthman as stated in the hadith of al-Bayhaqi, so the amount is not essential to follow the sunnah of the prophet().
The sunnah of the prophet () was reported by Hudhaifah (see for example here in Sunan an-Nasa-i).
It was narrated that Hudhaifah said:
"I prayed with the Messenger of Allah (ﷺ) one night. He started reciting Surat Al-Baqarah and he recited one hundred verses, then did not bow, rather he continued. I thought: 'He will complete it in two rak'ahs, but he continued.' I thought: 'He will complete it and then bow,' but he continued until he recited Surat An-Nisa', then Al Imran. Then he bowed for almost as long as he had stood, saying while bowing: 'Subhan Rabbial-azim, Subhan Rabbial-azim, Subhan Rabbial-azim ( Glory be to my Lord Almighty, Glory be to my Lord Almighty, Glory be to my Lord Almighty).' Then he raised his head and said: 'Sami Allahu liman hamidah (Allah hears the one who praises Him). Then he prostrated and made his prostration lengthy, saying: "Subhan Rabbial-A'la, Subhan Rabbial-A'la, Subhan Rabbial-A'la (Glory be to my Lord Most High, Glory be to my Lord Most High, Glory be to my Lord Most High). And he did not come to any verse that spoke of fear or glorifying Allah, the Mighty and Sublime, but he said something appropriate."
Note that the prophet () in other narratives explained that the night prayer (and taraweeh is a night prayer) is performed as set's of two raka'a.
So what is the explanation of the amount then?
Standing for the sahabah and tabi'in during such a long recitation was too hard, it is reported that 'Umar has chosen different imam's and would ask the imam who recited quickly to recite in each raka'a 40 verses, the imam who's recitation is slow and lengthy would be asked to perform a ruku' after 20 verses and the one in the middle after 30 verses.
So as it was too hard to stay for such a long term the length of recitation was shortened and replaced by a higher amount of raka'as.
So be aware if you finish taraweeh in half an hour or less that you are far away from the sunnah of the prophet() and the path his sahbah followed.