Af writes a plain f and continues the Semitic p. Its cognates are the Hebrew peh, the Syriac pe and the Arabic fa, and the set records a sound change that Ge'ez and Arabic made and Hebrew did not: in both southern branches the inherited p became f, while Hebrew kept the stop and allows it to soften to f only in certain positions.
Everything odd about the end of the Ge'ez order follows from that change. A language with no p has no need of a letter for one, so the twenty-two inherited signs contained none. When Greek names and Greek loanwords arrived with the scriptures, the language met a sound it had lost and a body of proper names it could not spell. The two p letters at the end of the order, payt and psa, are the answer to that problem, and they stand at the end because they were added to a sequence already fixed.
So this letter is where a reader should start when asking why the fidel has twenty-six letters rather than twenty-two. Two of the four additions, harm and sappa, are inheritances from a South Arabian script richer than the Northwest Semitic one. The other two are repairs, made after the fact, for a gap this sound change opened.
The change also explains why English speakers meet Ethiopian names in forms that look unrelated to their Greek or Hebrew originals. A name arriving with a p is not transliterated with one, and the f standing in its place is not an approximation made by a foreign ear. It is the regular reflex of a sound change internal to the language.