Does Qur'an 5:48 imply that Allah wants Jews to follow the Torah and Christians to follow the Gospel ...
Yes.
... instead of the Qur'an?
No.
Al-Ma'idah 5:44 clearly stipulates that Allah is referring to the Torah that Allah has sent down, not the one that has been corrupted; only the one revealed by Allah.
إِنَّا أَنزَلْنَا التَّوْرَاةَ فِيهَا هُدًى وَنُورٌ ۚ يَحْكُمُ بِهَا النَّبِيُّونَ الَّذِينَ أَسْلَمُوا لِلَّذِينَ هَادُوا وَالرَّبَّانِيُّونَ وَالْأَحْبَارُ بِمَا اسْتُحْفِظُوا مِن كِتَابِ اللَّهِ وَكَانُوا عَلَيْهِ شُهَدَاءَ ۚ فَلَا تَخْشَوُا النَّاسَ وَاخْشَوْنِ وَلَا تَشْتَرُوا بِآيَاتِي ثَمَنًا قَلِيلًا ۚ وَمَن لَّمْ يَحْكُم بِمَا أَنزَلَ اللَّهُ فَأُولَٰئِكَ هُمُ الْكَافِرُونَ
Indeed, We sent down the Torah, in which was guidance and light. The prophets who submitted [to Allah] judged by it for the Jews, as did the rabbis and scholars by that with which they were entrusted of the Scripture of Allah, and they were witnesses thereto. So do not fear the people but fear Me, and do not exchange My verses for a small price. And whoever does not judge by what Allah has revealed — then it is those who are the disbelievers.
Al-Ma'idah 5:44
From an Islamic point of view, the verses here do not refer to the Torah commonly referred to as the first five books of the Old Testament.
The same applies to Al-Ma'idah 5:47; it is about what Allah has revealed, not the books (the four Gospels of Matthew, Mark, Luke, and John) that are commonly accepted as the Gospels today, and of course not the epistles of Paul or any other books in the New Testament it its current form.
وَلْيَحْكُمْ أَهْلُ الْإِنجِيلِ بِمَا أَنزَلَ اللَّهُ فِيهِ ۚ وَمَن لَّمْ يَحْكُم بِمَا أَنزَلَ اللَّهُ فَأُولَٰئِكَ هُمُ الْفَاسِقُونَ
And let the People of the Gospel judge by what Allah has revealed therein. And whoever does not judge by what Allah has revealed — then it is those who are the defiantly disobedient.
Al-Ma'idah 5:47
If Christians and Jews follow what Allah has revealed in their books, they would follow the Prophet ﷺ:
الَّذِينَ يَتَّبِعُونَ الرَّسُولَ النَّبِيَّ الْأُمِّيَّ الَّذِي يَجِدُونَهُ مَكْتُوبًا عِندَهُمْ فِي التَّوْرَاةِ وَالْإِنجِيلِ
Those who follow the Messenger, the unlettered prophet, whom they find written in what they have of the Torah and the Gospel
Al-A'raf [7:157]
They would believe in the Prophet ﷺ, honor him, support him, and follow the light [Qur'an, same as what the Torah is called in Al-Ma'idah 5:44]
فَالَّذِينَ آمَنُوا بِهِ وَعَزَّرُوهُ وَنَصَرُوهُ وَاتَّبَعُوا النُّورَ الَّذِي أُنزِلَ مَعَهُ ۙ أُولَٰئِكَ هُمُ الْمُفْلِحُونَ
So they who have believed in him, honored him, supported him and followed the light which was sent down with him — it is those who will be the successful.
Al-A'raf [7:157]
The Jews know the Prophet ﷺ that was described in their books as they know their own offspring (see Surah Al-Baqarah [2:146]). In fact, Allah tells us in Al-Ma'idah [5:68] that unless they uphold the Torah and the Gospel that Allah has revealed to them, they will surely increase in transgression and disbelief. Every time the Torah and the Gospel are mentioned in the Qur'an in the sense of them being guides or lights or to be followed, the condition of "as revealed" is added. Even in verses referring to Prophet 'Issa ﷺ talking about the Torah, the phrase the Torah in his hands (Arabic: مُصَدِّقًا لِّمَا بَيْنَ يَدَيْهِ) is used as in Al-Ma'idah 5:46-47.
So, yes, the Jews and Christians should uphold what they find in the Torah and Gospel that Allah revealed, which would lead them to follow the Qur'an, not substitute the Qur'an with the Torah and the Gospel they have today.
Al-Ma'idah 5:48 does not imply the use of the Torah or the Gospel. On the contrary, it is saying that the Book [Qur'an] was revealed by Allah confirming (only confirming) what was previously revealed and declaring that the Qur'an is the sole criterion (Arabic: مُهَيْمِنًا عَلَيْهِ) over other books. It also instructed him not to not follow their inclinations, and that for every nation there was a law and a methodology (Arabic: شِرْعَةً وَمِنْهَاجًا). So the Prophet ﷺ judge between them by what Allah has revealed to him (Arabic: فَاحْكُم بَيْنَهُم بِمَا أَنزَلَ اللَّهُ), which is the Qur'an.
