Albedo is totally loyal to Ainz and, NO, she doesn't act like a child on her first day of school. She's in love with Ainz because she programmed (edited) by Ainz when the servers closed (in fact her previous programming was to be a nymphomaniac), but her love is more of a sadistic love because she carries it in her programming, it's an obsession, and by itself, on the cover image of this game, it shows a shy Albedo that seems to be being harassed. Bad start.
Albedo is jealous when it comes to Ainz, but she's not a shy girl, she's a LEADER who, first and foremost, serves her master obediently, even though that means having to face the other floor guards. In the end, he does not reproach that other floor guards, such as Shalltear, may also become Ainz's wives because he considers that his master may have several wives or concubines.
In short, Albedo is not shy, as you see in the game. Above all, she's a devil and a maximum authority, that's why, with Koikatu, Albedo is not achieved, and if it's not achieved, you can't get into an Overlord story.
Saying Albedo does not act like a schoolgirl is a
big overstatement which kind of shows you probably did not read the LN, which there is nothing wrong with that.
Albedo has literally body pillowS of Momonga, in the anime this is shown and also how she uses them, not much different from a schoolgirl's love I'd say.
If you have read the LN...
As for how she behaves with other floor guardians, she is an overseer, I know this much. She
will act childish in some instances but will stop right away when she needs to be serious. Her overseer abilities are never put in question and everyone obeys her.
The only exception which shows another "Schoolgirl" behavior is when Demiurge disagrees with letting Ainz go alone, at least in the anime, her reply is pretty school-girl like.
^So, when is all this shown in the game? Almost never, so far.
You really have to pay attention to the dialogue to get it (And even so, I do not remember how far R2 goes), her behavior towards other NPCs will be shown without any hints in the mirror, a token added in R4 to show extra scenes.
Those extra scenes are NPCs interacting with each other since the rest of the game is from a first person perspective (Ainz's perspective).
So will Albedo be sadistic then? Eh, not really.
Reality is that Albedo is never truly sadistic, there is no way anyone would put her into question: Floor guardians seek orders from her, also shown in the anime when Demiurge wants his order, and she does
a lot of background stuff, so much so that if she were to leave Nazarick to go to E-rantel with Ainz, someone would need to take her place, someone like Cocytus or Demiurge.
She would probably be sadistic if they did not respect her or her orders but that never happens (Which is good for Nazarick to work properly).
So, does she, at the very least, act sadistic outside of work with other members? Sorry but no.
Even if you had not read the LN, just watch the anime with the bicorn scene, which by the way looks like a day out with fellow
school girls.
The more you read the LN/Watch the anime, the more you will see that Nazarick members are chill with each other, for the most part. They have to consider each other allies and respect each other and their roles if they do not want everyting to fall apart.
If you have read the LN...
If you want to see a HINT of Albedo being sadistic, bring her to carne village (R3?) with you and then do her route (R4).
At least some sentences will hint at her hate towards "insects" but you can get her full opinion about humans if you will also bring her to E-rantel in (hopefully) R5.
If you read thus far, you will be wondering, what is up with the whole "Just hints" thing?
It is simple: I do not want to go too in-depth with character feelings, their ideas, their opinions, their dreams, (...) there is the LN for that and, for some stuff, even the anime.
I expect fans of at least one of those two to play this game and know all that stuff from the get-go, which is the whole reason why I also take the liberty to skip the whole Carne Village fight and NPC interactions (in which Albedo would act sadistic towards humans). She will still
hint at the key elements, though.
The reason why I do all this skipping is not because I am lazy but simply because all that stuff is
boring.
Do not get me wrong, it is funny in the anime, it is funny in the LN but this is neither of those, this is a HENTAI game made by a fan in less than a month (1 month in a week! \o/).
The main focus will always be hentai where possible and things people may like (hence why of the Victim's new appearance, no one likes fetuses, I hope).
I could have took the easier route and make a trainer game but exactly because I am a fan I want to stay true to the lore as much as possible but if I will ever need to face the choice between 100% lore and hentai, I will always choose hentai like the true pervert I am.