For the purpose of the damage type swap feature of the Order of Scribes Wizard's Awakened Spellbook feature, does the +1 bonus to damage rolls from the Magic Weapon spell qualify as bludgeoning/slashing/piercing damage?
Magic Weapon has no damage type
The magic weapon spell description says:
You touch a nonmagical weapon. Until the spell ends, that weapon becomes a magic weapon with a +1 bonus to attack rolls and damage rolls.
The spell does not mention any damage type, and has no damage type. The weapon that is enchanted has a damage type, and the additional damage will be of the weapon's, not the spell's type.
Therefore, there is nothing to swap here with Awakened Spellbook.