@Snowmirror The wait is now over, so let's take a look at Anput.
Looks
The least interesting? She's a girl with a jackal for a head! If that's not interesting, then what is? Seriously, that is a very interesting design choice and something that you definitely don't see every day. When most people think about animal people, they either think "cute waifu anime girl with ears and a tail" or "sexy furry anthropomorphic animal" so you have no idea how refreshing it is to see an animal person design that is not inherently sexual.
Because Anput's race is so different, I think putting her weight is important. Are Inpu naturally heavier than humans? Lighter? Or is their weight generally on par with humans of the same size?
Also, not a critique but just a suggestion: I think you should put an identifying mark that's inherent to her race like how Kamith has his sun and moon marks. It'll make Anput more visually interesting, and distinguish her from others of her race. I popped over to the Inpu's page, and I see that they all are relatively similar, so I think Anput needs something that helps her stand out. Some jewelry? A tattoo? Maybe a scar that she received as she was escaping from her country?
Nature
Her mannerisms are good, but I was wondering about her patting her dress: what exactly does that mean? Not to say it's bad, but I just can't picture it in my head.
Her motives, what sense of justice did she develop? Does she want revenge? Does she now think that killing enemies is wrong? This is the part where your character breaks down somewhat. She's a main character, so unless this is a character-driven story with a plot that is only designed to further the characters, Anput really needs a motive that drives her character towards a goal. I know that she hates her government, but what of it? Does she want revenge against them? Does she think that it's corrupt and wants it overthrown? Think of motivations as the driving force of a character in a story towards a tangible goal. By the stories end, where will she end up? What would she have accomplished, or even failed to do? This is especially important when there are multiple main characters at once; if one doesn't have any goals, the other characters will overtake her in importance and precedence, and she'll just fade into the background. The motives that she has now are too vague to be anything that is driving her towards something. They make sense from a character perspective, but from a story perspective, she needs something more concrete.
In what ways is she self-righteous, as in, what exactly does she believe that she thinks that others would benefit from if only they'd just listen to her? And in what ways is she hypocritical? I saw that even though she dislikes her government, she's still fond of her country, so that's something, but is there anything else? Just explain that, and her flaws are golden.
It's just my opinion, but I think her prejudice would be more streamlined and make more sense in you just said that she distrusts government in general. It would make sense for her character. After all, she doesn't trust Seamline or the Wilds, and she ran away from her own government after what they did to her mother, so I don't see a character like that trusting anyone.
What about detective work is she good at? While I only know about it from Batman and Detective Pikachu, I know that quite a bit goes into it. Is she good at interrogating people? Sniffing out clues (pun totally intended)? Deductive reasoning? Be a bit more specific. Also, does her talent for embalming ever come in handy in her line of work? I don't see how it could, but if I may I wanna make a suggestion. You know what other skill that she would have most likely learned as an embalmer? How to prep a dead body. And you know what that would help with? Identifying causes of death.
No complaints about her hobbies.
You said that she's naturally kind and generous, but she's also fake; how does that work? Does she overcompensate to make people like her more? I know that you said that she has a hard time maintaining this around people that she doesn't like, but that's true for anyone, so there must be something more to it if she can reasonably be described as "fake". All other problems that I had in her flaws also apply here. Other than that, she has a strong personality; she just needs a solid framework to hang it on, that framework being her primary objective.
Social
Is there something special about the flower crystal? I saw on its item page that it was given to her by someone important to her, but does it do anything? Does she do anything with it?
She's a jackal-headed former priestess of a death god who shoots guns? In the 1910s? Where do I get in line to pre-order? Seriously, make this girl the badass that I know she is! Give her a warrior culture schtick or something. I know it's a little cliche, but honestly, at this point, her character could benefit from a cliche or two.
Also, as an aside, do normal humans exist in this world and does this detective agency interact with them? I'm gonna assume that it does, and I apologize if I was already supposed to know this, I forgot something in between critiques. But if so, what trials and tribulations does Anput face being so obviously abnormal? And even among magical kind, does she ever face any prejudice or downright racism? How does she move among normal people? Does she have to wear a hood? Is there a magical glamour that makes her seem human? How does she feel about her appearance? is she proud of her looks and doesn't care what anyone else thinks? Or does she sometimes feel like a freak? What are the beauty standards of her race? Would she have been considered beautiful to her people? If so, is there any dissonance that she has to endure living among people who might not think the same? Just some food for thought.
History
Solid. That's a backstory is I ever saw one. Having to embalm one's own mother? Couldn't be me. A+!
So all in all, Anput is a good character, but I think the problem that you're having is that she doesn't have a solid motivation that makes her relevant to not just the plot, but her own group of partners/friends. What goals are they working towards, and how does her goal differ from it? Therein lies the drama, and as we all know, stories are driven by drama. Now, I don't wanna be insensitive to Anput and her kind, so I'm not gonna give her something like dog treats or a bone. Inpu are people, so I'll give her this flower sticker since she seems to like them ❤️️