Quran: it is legal to seek Mut'ah (istimta’ - verb form of Mut'ah)
Quran: Surah An-Nisa (4:24)
Translation: Qarai

and married women, excepting your slave-women. This is Allah’s ordinance for you. As to others than these, it is lawful for you to seek [temporary union with them] with your wealth, in wedlock, not in license. For the enjoyment you have had from them thereby, give them their dowries, by way of settlement, and there is no sin upon you in what you may agree upon after the settlement. Indeed Allah is all-knowing, all-wise.

Translation: Sarwar

You are forbidden to marry married women except your slave-girls. This is the decree of God. Besides these, it is lawful for you to marry other women if you pay their dower, maintain chastity and do not commit indecency. If you [mut'ah] marry them for the appointed time you must pay their dowries. There is no harm if you reach an understanding among yourselves about the dowry, God is All-knowing and All-wise.

Translation: Abdul Haleem

women already married, other than your slaves. God has ordained all this for you. Other women are lawful to you, so long as you seek them in marriage, with gifts from your property, looking for wedlock rather than fornication. If you wish to enjoy women through [mut'ah] marriage, give them their bride-gift- this is obligatory- though if you should choose mutually, after fulfilling this obligation, to do otherwise [with the bride-gift], you will not be blamed: God is all knowing and all wise.

وَٱلْمُحْصَنَتُ مِنَ ٱلنِّسَآءِ إِلَّا مَا مَلَكَتْ أَيْمَنُكُمْ ۖ كِتَبَ ٱللَّهِ عَلَيْكُمْ ۚ وَأُحِلَّ لَكُم مَّا وَرَآءَ ذَلِكُمْ أَن تَبْتَغُوا۟ بِأَمْوَلِكُم مُّحْصِنِينَ غَيْرَ مُسَفِحِينَ ۚ فَمَا ٱسْتَمْتَعْتُم بِهِۦ مِنْهُنَّ فَـَٔاتُوهُنَّ أُجُورَهُنَّ فَرِيضَةًۭ ۚ وَلَا جُنَاحَ عَلَيْكُمْ فِيمَا تَرَضَيْتُم بِهِۦ مِنۢ بَعْدِ ٱلْفَرِيضَةِ ۚ إِنَّ ٱللَّهَ كَانَ عَلِيمًا حَكِيمًۭا

Note: The Arabic word used for marriage in this verse is Istimta’tum (verb form of Mut'ah), not Zawajtum (permanent marriage).

The companions engaged in Mut'ah at the direction of the Holy Prophet (ﷺ)

Reference: Sahih Muslim 1404a

Sahih Muslim 1404a
Abdullah (b. Mas'ud) reported:

We were on an expedition with Allah's Messenger (ﷺ) and we had no women with us. We said: Should we not have ourselves castrated? He (the Holy Prophet) forbade us to do so He then granted us permission that we should contract temporary marriage for a stipulated period giving her a garment, and 'Abdullah then recited this verse: 'Those who believe do not make unlawful the good things which Allah has made lawful for you, and do not transgress. Allah does not like trangressers" (al-Qur'an, 5:87).

حَدَّثَنَا مُحَمَّدُ بْنُ عَبْدِ اللَّهِ بْنِ نُمَيْرٍ الْهَمْدَانِيُّ، حَدَّثَنَا أَبِي وَوَكِيعٌ، وَابْنُ، بِشْرٍ عَنْ إِسْمَاعِيلَ، عَنْ قَيْسٍ، قَالَ سَمِعْتُ عَبْدَ اللَّهِ، يَقُولُ كُنَّا نَغْزُو مَعَ رَسُولِ اللَّهِ صلى الله عليه وسلم لَيْسَ لَنَا نِسَاءٌ فَقُلْنَا أَلاَ نَسْتَخْصِي فَنَهَانَا عَنْ ذَلِكَ ثُمَّ رَخَّصَ لَنَا أَنْ نَنْكِحَ الْمَرْأَةَ بِالثَّوْبِ إِلَى أَجَلٍ ثُمَّ قَرَأَ عَبْدُ اللَّهِ ‏{‏ يَا أَيُّهَا الَّذِينَ آمَنُوا لاَ تُحَرِّمُوا طَيِّبَاتِ مَا أَحَلَّ اللَّهُ لَكُمْ وَلاَ تَعْتَدُوا إِنَّ اللَّهَ لاَ يُحِبُّ الْمُعْتَدِينَ‏}‏ ‏.‏
Reference  : Sahih Muslim 1404a
In-book reference  : Book 16, Hadith 13
The abrogation of Mut'ah at Khaibar, was limited to the campaign of Khaibar.
Jami` at-Tirmidhi 1794
Narrated 'Abdullah and Al-Hasan, the sons of Muhammad bin 'Ali:

From their father, that 'Ali said: "During the time of Khaibar, the Messenger of Allah (ﷺ) prohibited Mut'ah with women and eating the meat of domesticated donkeys.

حَدَّثَنَا مُحَمَّدُ بْنُ بَشَّارٍ، حَدَّثَنَا عَبْدُ الْوَهَّابِ الثَّقَفِيُّ، عَنْ يَحْيَى بْنِ سَعِيدٍ الأَنْصَارِيِّ، عَنْ مَالِكِ بْنِ أَنَسٍ، عَنِ الزُّهْرِيِّ، ح وَحَدَّثَنَا ابْنُ أَبِي عُمَرَ، حَدَّثَنَا سُفْيَانُ بْنُ عُيَيْنَةَ، عَنِ الزُّهْرِيِّ، عَنْ عَبْدِ اللَّهِ، وَالْحَسَنِ، ابْنَىْ مُحَمَّدِ بْنِ عَلِيٍّ عَنْ أَبِيهِمَا، عَنْ عَلِيٍّ، قَالَ نَهَى رَسُولُ اللَّهِ صلى الله عليه وسلم عَنْ مُتْعَةِ النِّسَاءِ زَمَنَ خَيْبَرَ وَعَنْ لُحُومِ الْحُمُرِ الأَهْلِيَّةِ ‏.‏
Reference  : Jami` at-Tirmidhi 1794
In-book reference  : Book 25, Hadith 7
Mut'ah continued to be practiced in the time of Abu Bakr and the beginning of Umar's khilafat

Reference: Sahih Muslim 1405c

Sahih Muslim 1405c
Ibn Uraij reported:

'Ati' reported that Jabir b. Abdullah came to perform 'Umra, and we came to his abode, and the people asked him about different things, and then they made a mention of temporary marriage, whereupon he said: Yes, we had been benefiting ourselves by this temporary marriage during the lifetime of the Prophet (ﷺ) and during the time of Abu Bakr and 'Umar.

وَحَدَّثَنَا الْحَسَنُ الْحُلْوَانِيُّ، حَدَّثَنَا عَبْدُ الرَّزَّاقِ، أَخْبَرَنَا ابْنُ جُرَيْجٍ، قَالَ قَالَ عَطَاءٌ قَدِمَ جَابِرُ بْنُ عَبْدِ اللَّهِ مُعْتَمِرًا فَجِئْنَاهُ فِي مَنْزِلِهِ فَسَأَلَهُ الْقَوْمُ عَنْ أَشْيَاءَ ثُمَّ ذَكَرُوا الْمُتْعَةَ فَقَالَ نَعَمِ اسْتَمْتَعْنَا عَلَى عَهْدِ رَسُولِ اللَّهِ صلى الله عليه وسلم وَأَبِي بَكْرٍ وَعُمَرَ ‏.‏
Reference  : Sahih Muslim 1405c
In-book reference  : Book 16, Hadith 18

Note the use of Istamta'na in this hadith

Note also that Jabir bin Abdullah is amongst the most prominent of companions.

Umar forbade Mut'ah

Reference: Sahih Muslim 1249

Sahih Muslim 1249
Abd Nadra reported:

While I was in the company of Jibir, a person came and said: There is difference of opinion amomg Ibn Abbas and Ibn Zubair about two Mut'as (benefits, Tamattul in Hajj and temporary marriage with women), whereupon jibir said: We have been doing this during the lifetime of Allah's Messenger (way peace be upon him), and then 'Umar forbade us to do so, and we never resorted to them.

حَدَّثَنِي حَامِدُ بْنُ عُمَرَ الْبَكْرَاوِيُّ، حَدَّثَنَا عَبْدُ الْوَاحِدِ، عَنْ عَاصِمٍ، عَنْ أَبِي نَضْرَةَ، قَالَ كُنْتُ عِنْدَ جَابِرِ بْنِ عَبْدِ اللَّهِ فَأَتَاهُ آتٍ فَقَالَ إِنَّ ابْنَ عَبَّاسٍ وَابْنَ الزُّبَيْرِ اخْتَلَفَا فِي الْمُتْعَتَيْنِ فَقَالَ جَابِرٌ فَعَلْنَاهُمَا مَعَ رَسُولِ اللَّهِ صلى الله عليه وسلم ثُمَّ نَهَانَا عَنْهُمَا عُمَرُ فَلَمْ نَعُدْ لَهُمَا ‏.
Reference  : Sahih Muslim 1249
In-book reference  : Book 15, Hadith 233
Umar: "This temporary marriage, had I come across it, I would have ordered stoning and done away with it!"
Muwatta Malik Book 28 Hadith 42
Yahla relates:

Yahya related to me from Malik from Ibn Shihab from Urwa ibn az- Zubayr that Khawla ibn Hakim came to Umar ibn al-Khattab and said, ''Rabia ibn Umayya made a temporary marriage with a woman and she is pregnant by him.'' Umar ibn al-Khattab went out in dismay dragging his cloak, saying, "This temporary marriage, had I come across it, I would have ordered stoning and done away with it! "

وَحَدَّثَنِي عَنْ مَالِكٍ، عَنِ ابْنِ شِهَابٍ، عَنْ عُرْوَةَ بْنِ الزُّبَيْرِ، أَنَّ خَوْلَةَ بِنْتَ حَكِيمٍ، دَخَلَتْ عَلَى عُمَرَ بْنِ الْخَطَّابِ فَقَالَتْ إِنَّ رَبِيعَةَ بْنَ أُمَيَّةَ اسْتَمْتَعَ بِامْرَأَةٍ فَحَمَلَتْ مِنْهُ ‏.‏ فَخَرَجَ عُمَرُ بْنُ الْخَطَّابِ فَزِعًا يَجُرُّ رِدَاءَهُ فَقَالَ هَذِهِ الْمُتْعَةُ وَلَوْ كُنْتُ تَقَدَّمْتُ فِيهَا لَرَجَمْتُ ‏.
Reference  : Muwatta Malik Book 28 Hadith 42
Arabic reference  : Book 28, Hadith 1137

Note the use of Istamta' in this hadith. Note also that Umar does not assert the Prophet prohibited it.

Imran bin Hussain: Abgoration of Mut'ah was Umar's own inclination. It was not prohibited by the Prophet (ﷺ).

Reference: Sahih al-Bukhari 4518

Sahih al-Bukhari 4518
Narrated `Imran bin Husain:

The Verse of Muta was revealed in Allah's Book, so we performed it with Allah's Messenger (ﷺ), and nothing was revealed in Qur'an to make it illegal, nor did the Prophet (ﷺ) prohibit it till he died. But the man (who regarded it illegal) just expressed what his own mind suggested.

حَدَّثَنَا مُسَدَّدٌ، حَدَّثَنَا يَحْيَى، عَنْ عِمْرَانَ أَبِي بَكْرٍ، حَدَّثَنَا أَبُو رَجَاءٍ، عَنْ عِمْرَانَ بْنِ حُصَيْنٍ ـ رضى الله عنهما ـ قَالَ أُنْزِلَتْ آيَةُ الْمُتْعَةِ فِي كِتَابِ اللَّهِ فَفَعَلْنَاهَا مَعَ رَسُولِ اللَّهِ صلى الله عليه وسلم، وَلَمْ يُنْزَلْ قُرْآنٌ يُحَرِّمُهُ، وَلَمْ يَنْهَ عَنْهَا حَتَّى مَاتَ قَالَ رَجُلٌ بِرَأْيِهِ مَا شَاءَ‏.‏
Reference  : Sahih al-Bukhari 4518
In-book reference  : Book 65, Hadith 43

Note the word in Arabic is Mut'ah, and is not in any way specific to Hajj at-Tamattu. Common English translations misrepresent the translation of this hadith.

Quran: Do not forbid the good things that Allah has made lawful for you.
Quran: Surah Al-Ma'idah (5:87)
Translation: Saheeh International

O you who have believed, do not prohibit the good things which Allah has made lawful to you and do not transgress. Indeed, Allah does not like transgressors.

‏يَٓأَيُّهَا ٱلَّذِينَ ءَامَنُوا۟ لَا تُحَرِّمُوا۟ طَيِّبَتِ مَآ أَحَلَّ ٱللَّهُ لَكُمْ وَلَا تَعْتَدُوٓا۟ ۚ إِنَّ ٱللَّهَ لَا يُحِبُّ ٱلْمُعْتَدِينَ