Our interpretation of La Nabi Ba'di to mean no prophet that is in opposition to the Shari'ah of the Prophet and is not his follower in totality is not extraneous, it can be derived strictly from the plain wording itself.
Ba'd is usually translated in English "after" but that does not encompass its full meaning, nor is it necessary that ba'd always means after in the sequential sense.
It is perfectly legitimate in Arabic language to interpret the word Ba'd to mean that which is in contrast to, in opposition to - as opposed to that which accords with and is in conformity with.
A perfect example of this from the Holy Quran:
فَبِاَیِّ حَدِیۡثٍۭ بَعۡدَہٗ یُؤۡمِنُوۡنَ
In what discourse then, after this, will they believe?
Incidentally, the Quran-only heretics consider this Ayah their most devastating weapon in their arsenal in repudiating the following of the Ahadith. The Quran refers to itself as Hadith, and is apparently asking a rhetorical question that in which Hadith after this [Quran] will you believe, meaning don't believe in any Hadith other than the Quran. On the surface it seems like a pretty solid argument for the Quranists/Hadith-rejecters.
But the correct interpretation of this Ayah, based on an alternative but bona fide meaning of the word ba'd is essentially not to believe in any opposing or contrary narrative to the Quran, not that every narration subsequent to the Quran in chronology and sequence is false even if that narration is in accord with the Quran and falling under its overall authority.
Likewise, the statement "There is no Prophet after me" really and truly means don't believe in any Prophesy-claimant after me who doesn't conform to me, who isn't subordinate to me, and who doesn't recognize me as supreme - I am the Seal of the Prophets.