Without any context or prior knowledge of the series, this is objectification in the literal sense.
I wouldn't blame anyone for getting the wrong impression.
If this was the only circumstance that involved Kazooie in Smash, you'd be correct however, she's very involved with their playstyle as I am sure you have witnessed.
If we take a look at Oxford's definition since we're on the subject of the literal sense:
verb
verb: objectify; 3rd person present: objectifies; past tense: objectified; past participle: objectified; gerund or present participle: objectifying
1.
degrade to the status of a mere object.
"a deeply sexist attitude that objectifies women"
2.
express (something abstract) in a concrete form.
"good poetry objectifies feeling"
I wanna focus on the first one. When objectifying someone or something, you are dehumanizing them (and I know that Kazooie's not a human but my point stands) to the point of being inessential. This is pretty much disproved with how much presence Kazooie has in Smash. Her name is mentioned on the fighters pass, her head shows up on the BK stock icon, the announcer refers to them both by name and not just "Banjo" and her utilities and what she has to offer consists of half their moveset (I'm just assuming it's half, haven't been counting). It's evident that they knew how important she is and how much of an injustice it would be to just treat her as just a "tool". If that's the case, why do they bother mentioning her?
Now about the Pack Whack. The Pack Whack is fukken awesome. And look at her face in that picture you shared. That's the face of consent right there. One thing that you have to keep in mind though that it's still just a quirky and silly move from a quirky and silly children's game being referenced in a current and more modern quirky and silly children's game. I do not think the developers were thinking about objectifying her when the idea of this move came into fruition but I do think that they were just figuring out ways to add more abilities by the time Banjo-Tooie was in development. The Pack Whack wasn't a thing in the first game. It's fun. It looks silly. It's very PG orientated and it's proven to be effective.
The thing is, video games are a form of art and things are going to get
very subjective especially on the topic of first impressions. I wouldn't blame anyone for getting the wrong impression either. I will blame them though if they decide to ignore reason coming from those that have actually played the BK games when trying to explain that their impression may not be the case. I don't expect anyone that hasn't played the games to get into them, and I'm not gonna push that on anyone because I'm pretty sure some peoples minds here have been made up and that they don't really want to, and that's okay. That's why boomers like myself is hear to help you evaluate who the character is and what her purpose is.
And even after all that, if you still only see a tool or a weapon and you want to ignore the context that's been brought up many times, then where's the objectification coming from? Certainly not me. Highly doubtful it came from the developers making a children's game.
You are the one degrading her to a status of irrelevancy by comparing her to an inanimate object. You are the one dismissing the abilities and utilities Kazooie has to offer by just bringing up one example and going: "LOOK SHE'S BEING OBJECTIFIED". You are the one ignoring her and only seeing a bear. By the literal definition of the word, you are doing the objectification, which imo, is quite shameful especially (and ironically) at the expense of a female character in a thread that's essentially about Smash female activism.
(Now I don't mean YOU specifically, I'm moreso speaking about the general consensus some people share but hey, if the boot fits.)
And I'mma just add one last thing so my long winded post doesn't get taken outta context again like some of my previous posts I've made here:
I'm not trying to sell anyone on the idea of BK being the equivalent of a standalone female character because it involves Kazooie. I'm only trying to sell you on the fact that Kazooie exists, and she exists in the fighters pass. Duo or not, she's right there and there's no need to sweep her under the rug to get your agenda across.