Answer

I’m not sure that this is in fact the plain meaning of the verses. Beyond that, derash is also a legitimate way to derive Jewish laws from verses, and derash does not have to fit the plain meaning.
But beyond all that, it seems to me that such an interpretation of the verses is not far-fetched, since it says there, “from all that they instruct you,” and perhaps “from all” comes to include all of their directives.
Let’s look at the verses:
“If there arises a matter too difficult for you in judgment, between blood and blood, between claim and claim, and between plague and plague, matters of dispute in your gates, then you shall arise and go up to the place that the Lord your God shall choose. And you shall come to the Levitical priests and to the judge who will be in those days, and you shall inquire, and they shall tell you the matter of judgment. And you shall act according to the word that they tell you from that place which the Lord shall choose, and you shall take care to do according to all that they instruct you. According to the Torah that they instruct you and according to the judgment that they tell you, you shall do; you shall not deviate from the word that they tell you, right or left.”
The ending is that one must act according to the matter they tell you, and that relates to the disputed question or to the doubt. But afterward the verse continues: “and you shall take care to do according to all that they instruct you.” That is an unnecessary repetition, and one can understand it as referring to enactments and decrees. And certainly from the entire final verse, “According to the Torah that they instruct you…,” which is entirely superfluous, one can learn the authority of the sages.
And beyond that, there is the logical point that there must be a central authority that organizes religious practice. We can see today how problematic the situation is without one. That reasoning too can broaden the content of the verses and include enactments and decrees as well.
However, all this depends on the well-known dispute between Maimonides and Nachmanides: whether the source of authority for enactments and decrees is “do not deviate” (Maimonides in the first root and at the beginning of the Laws of Rebels), or whether that is the source only for authority in interpreting the Torah (Nachmanides in his glosses to the first root). If this refers only to interpretation of the verses, then it can be placed under the heading of doubts. When I have a doubt about the interpretation of the verse, they determine what the correct interpretation is. As for enactments and decrees, that of course does not fit.
Further, since we are obligated by what the verse commands, the sages only interpret the content of the command. For that, no essential authority is required, only the assumption that they are correct or represent the truth and justice (obviously they are not always correct). The obligation to act this way stems from the authority of the verse itself, not from the authority of the sages. Therefore Maimonides writes in chapter 2 of the Laws of Rebels that in order to disagree with a prior religious court on rabbinic laws, one must be greater than it in wisdom and number; but to disagree with a prior religious court regarding interpretation of the Torah, it is enough that it be the Great Court, and it need not be greater in wisdom and number. The explanation is that a dispute regarding enactments is a dispute about the authority of the previous religious court, since our obligation there stems from their own authority. In that case, greater wisdom and number are required in order to change it. But a dispute with a previous religious court regarding Torah law is not a dispute about their authority, because what we do there is by virtue of the authority of the verse, not the authority of the sages, who merely interpreted it.
May you be sealed for a good year