Sana'a manuscripts do not "prove" that Qur'an is corrupted. In fact, it actually proves that the Hadith about seven different Ahrufs and Qir'at is authentic.
The claims of Non-Muslims regarding Sana'a manuscripts have been thoroughly debunked here in this video:-
https://www.youtube.com/watch?v=3pcenpnMVVE
I have seen some examples of alleged "differences" in the Sana'a manuscripts and the standard Uthmanic text of the Glorious Qur'an and the "differences" are not that major. If we read the hadith scriptures, we shall realize that these kind of differences were common in early Islam and there is nothing so "shocking" about the discovery of Sana'a manuscripts.
In Bukhari, we can read:-
Narrated Ibn Mas`ud:
I heard a person reciting a (Qur'anic) Verse in a certain way, and I had heard the Prophet (ﷺ) reciting the same Verse in a different way. So I took him to the Prophet (ﷺ) and informed him of that but I noticed the sign of disapproval on his face, and then he said, "Both of you are correct, so don't differ, for the nations before you differed, so they were destroyed. (Sahih al-Bukhari 3476)
One of the principles of seven Ahrufs is that there might be some differences in the text and even different meaning. However, the difference is in the context of theme, not opposing or contradicting as Islamqa.info notes:-
"Secondly, what is meant by styles (ahruf, sing. harf)?
The best of the scholarly opinions concerning what is meant is that there are seven ways of reciting the Qur’aan, where the wording may differ but the meaning is the same; if there is a different meaning then it is by way of variations on a theme, not opposing and contradiction." (Source:- https://islamqa.info/en/answers/5142/the-revelation-of-the-quraan-in-seven-styles-ahruf-sing-harf)
We can interpret the findings of the Sana'a manuscripts in the light of seven Ahrufs, as it is possible to do so. This is because many of the variants fall under the category of seven ahrufs.
I will be using the following source in order to assess the variants in the Sana'a manuscripts:-
https://www.letmeturnthetables.com/2012/05/seven-ahruf-2-best-explanation-taqi.html
Here is a chart of some of the alleged "major differences" between the standard Uthmanic text and the Sana'a palimpsests:-

Here we can see that the so-called "major differences" are not even major differences at all and they all fall within the categories of seven ahrufs. They do not cause a major difference in the message of the Qur'an and all of them are within the categories of seven Qir'at and Ahrufs. This was already recorded in the hadith collection long before the Sana'a manuscripts were even discovered.
The differences fall under two categories:-
Variants that fall under the category of seven Ahrufs.
Differences that occurred due to scribal errors.
It should be noted that the Glorious Qur'an was transmitted by a mass number of people, so these scribal errors should only be treated as scribal errors only. As I mentioned earlier, the so-called "differences" are not major differences at all that cause a major difference in the message of the Glorious Qur'an.
You wrote:-
For example, in this post, the author claims that Quran knows the sex
of child is determined by father. However, منه could be منها and this
changes the entire conclusion invalid.
This does not matter at all. The context of the verse clearly shows that it is semen that is responsible for producing children. The Glorious Qur'an does not explicitly say X or Y chromosome; however, it still gives us a hint (i.e. it talks about semen).
منه refers to "from him"
منها means "from it"
The context of the Sura 75:39 suggests that it is talking about the process of development of fetus. It wouldn't matter if any of the words (منه or منها) were refering to fetus.
You wrote:-
Or in this video it's claimed that using اذا instead of ان is the key
point in understanding what Allah wanted to tell us. This is also
dependent on a word-based analysis and we can't be sure that this word
is truly اذا. Maybe it was ان and then it was changed/altered to اذا.
I checked the video, the interpretation of the person in the video here is based on English translation.
اذا means "when"
ان means "If"
This is not how Quran should be understood. You cannot interpret the glorious Qur'an in the light of English translation!
Here is an example of "If" being used instead of "when" in Surah 9:12:-
وَإِن نَّكَثُوا أَيْمَانَهُم مِّن بَعْدِ عَهْدِهِمْ وَطَعَنُوا فِي دِينِكُمْ فَقَاتِلُوا أَئِمَّةَ الْكُفْرِ إِنَّهُمْ لَا أَيْمَانَ لَهُمْ لَعَلَّهُمْ يَنتَهُون
This translates to:-
"And if they break their oaths from after their treaty...."
Both would work here.
The following examples would help understand what I am saying:-
"If a student breaks rules, he will be suspended."
"When a student breaks rules, he gets suspended."
Both would work.
I do not know why Islamophobes and haters of Islam pick such small differences and make such claims. I really do not know why Islamophobes and critics of Islam are raising such issues here when the fact of the matter is that there is no issue here at all!
It should be noted that Birmingham manuscripts prove that the Glorious Qur'an has been perfectly preserved and Birmingham manuscript is as old as Sana'a manuscripts.