The snafu of the Scribe Spell (about replacing a Spellbook without it) needs clarification − or maybe fixing or rethinking.
But I read the following part this way.
Because the spell duration is "Instantaneous", the effect of the spell is no longer magical.
In other words, magic was used to create the object. Afterward, the magic is done. The object itself isnt magic. (Compare the Create Water spell, where magic is used to create it, but the water itself is nonmagical and endures normally.)
The final result of the Scribe Spell spell is a NONMAGICAL SPELLBOOK.
Here a particular spell gets scribed into the Spellbook.
"
When the scribing is complete,
the spell becomes one of your known spells in the book,
appearing on its own page if the book was out of pages.
The spell appears in a cipher that is understandable only to you
or someone casting Identify or Scribe Spell,
and if the book was blank before the scribing,
that book is now your spellbook.
"
So, this is a "known" spell. Meaning it is a spell that one oneself knows, understands, and can rewrite over and over anywhere.
The problem is, nobody else understands the language that this spell is being written in. It is written in a unique "cipher" that only one person understands.
Other people can use magic to crack this code, namely Scribe Spell.
(Scribe Spell also mentions "Identify". The Identify spell description doesnt do anything like deciphering a code. I suspect, the general idea is supposed to be, a person casting Identify would understand what the gibberish is about, but still wouldnt "know" the spell.
But actually, here is the wording of Identify.
"You learn whether any spells are affecting the item."
− Well, no, there are no spells "affecting" the Spellbook.
"lf the item was created by a spell, you learn which spell created it."
− Well, yes. The Spellbook was "created by a spell". And the caster of Identify discovers magically, that Spellbook was created by the Scribe Spell spell.
But Wizards already know that Spellbooks are created by the Scribe Spell spell, so casting Identify here is moot.
The Identify spell description doesnt say what the Scribe Spell spell description seems to think it says.)