For example, if a single book with Efficiency V and Unbreaking III is used then the Mana Enchanter will only apply the Efficiency V enchant. I've tried it multiple times with various books and items and this seems to always happen.

"If any book has more than one enchantment, only the first will be accounted for."

Yes it is.

In https://github.com/Vazkii/Botania/blob/master/src/main/resources/assets/botania/lang/en_US.lang#L2574

Where is that said? It's nowhere in the Lexica Botania entry for the Mana Enchanter.

That's odd. The entry in Lexica Botania 228 only shows up to 7 on that. This is an issue with the Lexica then.

Quick edit; Here's a screenshot to show where it cuts off, at least for me.
http://i.imgur.com/Cmp9OT9.png