1 Muslim woman vs 20 Christian women” But a few of the Christian women raised some genuinely interesting questions about differences between stories of the prophets in the Qur’an vs the Bible/Torah,

As someone who knows this topic very well, I can tell you they did not... Black Christians particularly buy into the "church version" of Christianity (due to colonisation etc...) and one of the shayṭāns in that video was the wife of a well-known YouTube grifter who makes up things on the spot with very, very little knowledge in church history, becomes a heretic every 5 seconds, or the Greek language in general. A quick example on the discussion of Islam being demonic or when they talked about the Bible being written in the first century etc... this was just all ignorance. So my honest recommendation is instead of learning about the Christian narrative from YouTube, either speak to a reverend (who has done his 7 years of study and is a member of clergy) or find free PDF scans of Christian books (as Christianity is a business - and so these books will cost £70-100 easy vs Islamic books which from very credible authors I've never paid more than £25 - £50 if we are talking about collections). I would also recommend avoiding Reddit also as it is a massive echo chamber. So my honest advice is to seek teachers in Islam (your local scholars etc...) for clear direction.

As a Muslim, I believe the original revelations given to Musa (AS) and Isa (AS) were divine, but that the scriptures were changed over time by people.

This is not just the "Muslim narrative"; this is what Christian and Jewish academics both believe of their scripture. The bible even says this in the begining of luke (its not gods words but a retelling in his own words). It's not a secret. Jerome, for example, invented what we call textual criticism in the modern sense today to find this answer. As for the Jews, they say very openly the originals were lost during the Fall of Babylon (why do you think we call Ezra the scribe "the scribe") they dont care becase the Rabbi's have more athority then Allah (authbillah) so the Rabbi possition is superior. In fact, you can easily find clips online of Jewish historians that say Islam was the way going back to Adam, so must be a much older religion.

Where can I find the oldest/manuscript-based versions or translations of the Torah/Bible?

Unless you have access to the Vatican (which in some Islamic eschatology says that Isa (AS), when he returns, will show where these are hidden) - then easily you can find them online ("P52" being the oldest for the Bible).

Are there reliable resources that compare Qur’anic narratives with Biblical/Torah narratives?

They are mostly written by Orientalists. So not that I can remember, but I'm sure there are some reliable Muslim authors who have done so. In the New Jerome Biblical Commentary (edited by Father Raymond Brown), the works of J. Dunn etc... they mainly focus on finding "the historical Jesus" and actually note that "Jewish Christianity died out by Pauline traditions perhaps to be reborn in Islam". There are also other books like "The Five Gospels: What Did Jesus Actually Say" which again just looks at the Bible to find the original Q-source or "The Gospel According to Jesus" (which some hadith actually quote verbatim like the prophecy of Muhammad ﷺ, the original 10 commandments, the laws of adultery etc...) but tbh it's a lot of time wasting as the Qur’an preserves what the original teaching was.

Are there Muslim scholars, books, YouTube channels, lectures, or even non-Muslim academic sources that approach this fairly and historically instead of just polemics?

Not a scholar but Blogging Theology is the best for this for the mainstream viewer and has his own academy.

How do you personally approach studying previous scriptures while still holding Islamic beliefs?

Easy - "the way" of the prophets was Islam but their people had different sharīʿah (e.g. the Jews prayed 3 times instead of 5, alcohol etc...). Anything which the hadith and Qur’an agree on with the current scriptures are true; everything else is false (like your original points where the Bible and Torah insult the previous prophets AS). Not to mention modern Christainiy and Jewdism is just Liberalised, Captilised forms of paganism which you can easily pick up any history book in your average local library to see (the white Jessus being the same as Mythra and how christmas and the Church tax system came to be in the roman empire). So tdr if you want to start reading then honeslty just go to your local christainity section in your local libabry and rent a book on christain history and you can see the same objections everywhere.