I understand Lapis much better now. Reading this long mission took me some time, but I liked it a lot.

Continuity error?
(“That’s definitely not canon, isn’t it?” asked Lapis.)
By putting it into parenthesis, did you intend to imply that Rayner is imagining this? Because she probably would, if she were there and listened to Nya’s tale, but last we know about Lapis is that she is elsewhere, listening to E.V.L.’s tale.

Some more errors:

“The only notable character who would try an all-out attack is The Boulder, and he certainly certainly isn’t subtle about anything.”

The agents watched as an gagged Elf was brought forth ...
“an” is only used when it’s easier to pronounce than “a”, so its “an elf”, not “a elf”, but still “a gagged elf”.

I decided to cut off the mission at the next major charge-worthy scene and and call it a day

HG

Nice touch, going a bit into your agents' history.

Errors:
1) “Sure, like you are so very good at it; leaving those ‘Nuggets’ in your bed…”
That semicolon should be a comma.

2) Being able to control powers is meaningless, when you can not control how you act
"Cannot" is one word, not two

3) Whomever made you do this, both his behavior and your response were totally uncalled for.
The correct word is "whoever;" the word is the subject of the verb "made", not the object.

4) “I leave in your hands to make sure she gets to her appointment alive."
There are some words missing: "I'll leave it in your hands ...

5) “Even if the notion of the cycle ceasing if the Avatar is killed in their Avatar State is true to canon,”
I believe you mean "even though," since it is canon that the cycle ends if the Avatar is killed while in the Avatar State. "Even if" implies that the upcoming phrase is not true, but that a contradiction would nonetheless exist were the premise true.

6) Lapis let out a squee that sounded like, “Minis!”, before catching herself.
Delete the commas.

7) While the girls began their next round, Rayner and Binary checked the Words, the former taking only a moment to side-ey the others.
Is that a misspelling, or a turn-of-phrase that I'm not familiar with?

8)court men dressed in silk roads
Since the text was not bold, I must assume that this was not from the badfic. The spelling error should be obvious.

Seeing how it culd have ben good, almost... very frustrating.

Character development was interesting, and I'm now pretty sure about who will be the leader for your special finish... and sme clues about the enemy.

Great writing, I'm sure the sequel will be as much good.