Was Muhammad allowed to issue religious teachings beyond Quran?

Throughout the Quran, God swears by different things, such as the moon (74:32), the position of the stars (56:75), and the Day of Resurrection (75:1). Yet, the most all-encompassing oath in the Quran occurs in Surah Al-Haaqqah (69), where God swears by everything.

[69:38] I swear by what you see. [69:39] And what you do not see.

(٣٨) فَلَآ أُقْسِمُ بِمَا تُبْصِرُونَ (٣٩) وَمَا لَا تُبْصِرُونَ

What is the reason for which God uses such a profound oath? The following verses reveal that God made this assurance to affirm the authenticity of the Quran as it was delivered by His messenger.

[69:40] This is the utterance of an honorable messenger. [69:41] Not the utterance of a poet; rarely do you believe. [69:42] Nor the utterance of a soothsayer; rarely do you take heed. [69:43] A revelation from the Lord of the universe.

(٤٠) إِنَّهُۥ لَقَوْلُ رَسُولٍ كَرِيمٍ (٤١) وَمَا هُوَ بِقَوْلِ شَاعِرٍ قَلِيلًا مَّا تُؤْمِنُونَ (٤٢) وَلَا بِقَوْلِ كَاهِنٍ قَلِيلًا مَّا تَذَكَّرُونَ (٤٣) تَنزِيلٌ مِّن رَّبِّ ٱلْعَـٰلَمِينَ

1	tanzīlun	تَنزِيلٌ	A revelation (tanzil)
2	min	مِّن	from
3	rabbi	رَّبِّ	(the) Lord (of)
4	l-ʿālamīna	ٱلْعَـٰلَمِينَ	the worlds / universe.

The word "Tanzil" ( تنْزيل ), used in Surah 69:43, confirms that the messenger's utterance mentioned in verses 69:40-42 refers explicitly to the Quran.

The verse then informs us that Muhammad was prohibited from uttering any other teachings aside from the Quran.

[69:44] Had he uttered any other teachings. [69:45] We would have punished him. [69:46] We would have stopped the revelations to him. [69:47] None of you could have helped him.

(٤٤) وَلَوْ تَقَوَّلَ عَلَيْنَا بَعْضَ ٱلْأَقَاوِيلِ (٤٥) لَأَخَذْنَا مِنْهُ بِٱلْيَمِينِ (٤٦) ثُمَّ لَقَطَعْنَا مِنْهُ ٱلْوَتِينَ (٤٧) فَمَا مِنكُم مِّنْ أَحَدٍ عَنْهُ حَـٰجِزِينَ

Here is the word-by-word breakdown of the above verses (44-47). In short, it is stating that if Muhammad uttered any other saying regarding the revelation (69:44), he would have been seized by the right hand (69:45) and had his aorta severed (69:46), and no one would have been able to help him (69:47).

44	1	وَلَوْ	And if	walaw
44	2	تَقَوَّلَ	he fabricated a lie / a saying	taqawwala
44	3	عَلَيْنَا	against us	ʿalaynā
44	4	بَعْضَ	some (other)	baʿḍa
44	5	ٱلْأَقَاوِيلِ	[the] words / sayings / commands / teachings,	l-aqāwīli
45	1	لَأَخَذْنَا	certainly we would have seized / taken / punished	la-akhadhnā
45	2	مِنْهُ	from him	min'hu
45	3	بِٱلْيَمِينِ	by the right hand.	bil-yamīni
46	1	ثُمَّ	Then	thumma
46	2	لَقَطَعْنَا	surely we would have cut off	laqaṭaʿnā
46	3	مِنْهُ	from him	min'hu
46	4	ٱلْوَتِينَ	the aorta.	l-watīna
47	1	فَمَا	And not	famā
47	2	مِنكُم	from you [all]	minkum
47	3	مِّنْ	any	min
47	4	أَحَدٍ	one	aḥadin
47	5	عَنْهُ	from him (are)	ʿanhu
47	6	حَـٰجِزِينَ	ones to prevent / stop (it).	ḥājizīna

This, in no uncertain terms, informs us that Muhammad could not utter any utterances regarding revelation aside from what was explicitly revealed to him by God in the Quran (Tanzil).

Some proof of this is that when Muhammad's contemporaries asked him a question regarding religion, he had to wait for the exact verse to be revealed to him with the answer.

[25:32] Those who disbelieved said, "Why did not the Quran come through him all at once?" We have released it to you gradually, in order to fix it in your memory. We have recited it in a specific sequence. [25:33] Whatever argument they come up with, we provide you with the truth, and a better understanding.

(٣٢) وَقَالَ ٱلَّذِينَ كَفَرُوا۟ لَوْلَا نُزِّلَ عَلَيْهِ ٱلْقُرْءَانُ جُمْلَةً وَٰحِدَةً كَذَٰلِكَ لِنُثَبِّتَ بِهِۦ فُؤَادَكَ وَرَتَّلْنَـٰهُ تَرْتِيلًا (٣٣) وَلَا يَأْتُونَكَ بِمَثَلٍ إِلَّا جِئْنَـٰكَ بِٱلْحَقِّ وَأَحْسَنَ تَفْسِيرًا

[20:114] Most Exalted is GOD, the only true King. Do not rush into uttering the Quran before it is revealed to you, and say, "My Lord, increase my knowledge."

(١١٤) فَتَعَـٰلَى ٱللَّهُ ٱلْمَلِكُ ٱلْحَقُّ وَلَا تَعْجَلْ بِٱلْقُرْءَانِ مِن قَبْلِ أَن يُقْضَىٰٓ إِلَيْكَ وَحْيُهُۥ وَقُل رَّبِّ زِدْنِى عِلْمًا

Also, this explains why the criticism against Muhammad by his contemporaries was the fact that he mostly listened.

[9:61] Some of them hurt the prophet by saying, "He is all ears!" Say, "It is better for you that he listens to you. He believes in GOD, and trusts the believers. He is a mercy for those among you who believe." Those who hurt GOD's messenger have incurred a painful retribution.

وَمِنْهُمُ ٱلَّذِينَ يُؤْذُونَ ٱلنَّبِىَّ وَيَقُولُونَ هُوَ أُذُنٌ قُلْ أُذُنُ خَيْرٍ لَّكُمْ يُؤْمِنُ بِٱللَّهِ وَيُؤْمِنُ لِلْمُؤْمِنِينَ وَرَحْمَةٌ لِّلَّذِينَ ءَامَنُوا۟ مِنكُمْ وَٱلَّذِينَ يُؤْذُونَ رَسُولَ ٱللَّهِ لَهُمْ عَذَابٌ أَلِيمٌ

And why it hurt the prophet when people attempted to engage him in lengthy conversations.

[33:53] O you who believe, do not enter the prophet's homes unless you are given permission to eat, nor shall you force such an invitation in any manner. If you are invited, you may enter. When you finish eating, you shall leave; do not engage him in lengthy conversations. This used to hurt the prophet, and he was too shy to tell you. But GOD does not shy away from the truth. If you have to ask his wives for something, ask them from behind a barrier. This is purer for your hearts and their hearts. You are not to hurt the messenger of GOD. You shall not marry his wives after him, for this would be a gross offense in the sight of GOD.

يَـٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوا۟ لَا تَدْخُلُوا۟ بُيُوتَ ٱلنَّبِىِّ إِلَّآ أَن يُؤْذَنَ لَكُمْ إِلَىٰ طَعَامٍ غَيْرَ نَـٰظِرِينَ إِنَىٰهُ وَلَـٰكِنْ إِذَا دُعِيتُمْ فَٱدْخُلُوا۟ فَإِذَا طَعِمْتُمْ فَٱنتَشِرُوا۟ وَلَا مُسْتَـْٔنِسِينَ لِحَدِيثٍ إِنَّ ذَٰلِكُمْ كَانَ يُؤْذِى ٱلنَّبِىَّ فَيَسْتَحْىِۦ مِنكُمْ وَٱللَّهُ لَا يَسْتَحْىِۦ مِنَ ٱلْحَقِّ وَإِذَا سَأَلْتُمُوهُنَّ مَتَـٰعًا فَسْـَٔلُوهُنَّ مِن وَرَآءِ حِجَابٍ ذَٰلِكُمْ أَطْهَرُ لِقُلُوبِكُمْ وَقُلُوبِهِنَّ وَمَا كَانَ لَكُمْ أَن تُؤْذُوا۟ رَسُولَ ٱللَّهِ وَلَآ أَن تَنكِحُوٓا۟ أَزْوَٰجَهُۥ مِنۢ بَعْدِهِۦٓ أَبَدًا إِنَّ ذَٰلِكُمْ كَانَ عِندَ ٱللَّهِ عَظِيمًا

All this shows that he was incredibly cautious about speaking about religion aside from what God revealed to him from the Quran. Yet, the Hadith records countless narrations being attributed to him, where he gives religious decrees left and right that are not found in the Quran. So either the Quran is wrong, or all these Hadith are false testimonies being attributed to him, and he did not make these supposed statements found in the Hadith literature. So people can go with the testimony and isnad of men or the testimony of God.

[6:19] Say, "Whose testimony is the greatest?" Say, "GOD's. He is the witness between me and you that this Quran has been inspired to me, to preach it to you and whomever it reaches. Indeed, you bear witness that there are other gods beside GOD." Say, "I do not testify as you do; there is only one god, and I disown your idolatry."

قُلْ أَىُّ شَىْءٍ أَكْبَرُ شَهَـٰدَةً قُلِ ٱللَّهُ شَهِيدٌۢ بَيْنِى وَبَيْنَكُمْ وَأُوحِىَ إِلَىَّ هَـٰذَا ٱلْقُرْءَانُ لِأُنذِرَكُم بِهِۦ وَمَنۢ بَلَغَ أَئِنَّكُمْ لَتَشْهَدُونَ أَنَّ مَعَ ٱللَّهِ ءَالِهَةً أُخْرَىٰ قُل لَّآ أَشْهَدُ قُلْ إِنَّمَا هُوَ إِلَـٰهٌ وَٰحِدٌ وَإِنَّنِى بَرِىٓءٌ مِّمَّا تُشْرِكُونَ