Sorry for the wall of text.
To not digress too much - Arita's remark is good as it's one more person who wouldn't mind Mitsuki opening up about her interests (and the author won't get comments pointing out that he's in the know).
--- animal talk below ---
I think it's a bit much to claim that it happens "worldwide", unless you've actually studied on this?
It was a generalization that in contrast to Japan other places may not emphasize animal-ness to the point shown in the previous paragraph, but comparisons to animals can still be found in other forms (not necessarily in the moe-kawaii flavor, not necessarily the types I listed equally represented - though I do think they're basic enough to have at least token presence everywhere - and not necessarily in the same manner for each country/region).
The first paragraph gives examples how loaded with meaning/traits certain animals are in Japan (it's then logical they'd find their way into everyday interactions as shorthands for said traits, and from there some may take them a bit more literally; trying to imagine a specific breed as a subcategory of unique traits might be out there too as an expansion of the original concept, but it may also be imported dog breed stereotypes mixed in). The second paragraph, which you could view as supplementary and not as a direct continuation of the answer, is what kinds of animal-calling you can find elsewhere instead (with specific examples being all idiomatic). I suspect we may not be in disagreement here?
And to clarify just in case - I also didn't mean getting accompanying vivid imagery of animals when looking at people (it's a visual trope specific to the medium, for chances of it happening to real people we'd have to ask neuroscience - or maybe psychology).
It's not a real expertise, just me putting together stuff starting with cultures I'm familiar with, what I've read on adjacent topics in the past (I have an interest in linguistics, if it amounts to anything) and checking for animal-related language in about two dozen languages from different parts of the world. If you live in a place where animals exist, and your language allows for similes/epithets, then it's inevitable somebody would combine the two together at some point, whatever the purpose of that may be. If there's a dominant culture or religion present that has a say on specific or even on all animals (praising or vilifying them, seeing them as equal to or strictly lower than humans, etc.), then that'd affect their use for that purpose accordingly.
I've encountered some studies on specific topics like why a branch of insults would be animal-related (it, possibly obviously, often boils down to the intent to dehumanize the recipient), but I don't recall anything thoroughly global in its scope. Nevertheless, I believe there should be some language evolution research out there on the use of comparisons to things our ancestors were familiar with in communication, and a different study on the prevalence of animals in symbolism, that would argue for those two being universal.
The reason I specifically used "pet" rather than "animal" in my comment was because in my country I've only heard of people being compared to animals in a derogatory way (pig, chicken etc.), as you and others mentioned. If I heard someone talking about dog or cat energy I'd think they've probably been influenced by US (or Japanese) media.
I did miss this implication, sorry for that.
I wasn't considering such a distinction because while some animals may be commonly taken as pets, they aren't universally pettable (just for dogs you have some breeds that are known to be cute or friendly, some that an average person considers scary/intimidating/more dangerous, wild or stray dogs that many would be wary of, some cultures that don't think of dogs fondly, in several languages a whelp and a puppy are a single word that also shares the former's meaning of an insolent child, "pet material" range differs from person to person, and so on), animals that aren't domesticated or suited for being pets, and the discussion started with why it's common to liken people to animals in manga (with dogs/puppies and cats being given as examples, and they're the most common, but comparisons to other animals happen too and you can also find ones that aren't flattering or cute among them, like somebody being seen as a barking/growling guard dog or students thinking a well-built teacher resembles a gorilla).
To me "you're as loyal as a dog" also seems insulting lol. It would sound to me like they're calling me a blindly obedient. I'm not sure if it's personal or cultural in this case, but, for the record, most of my family agreed.
It'd be "(as) faithful as a dog", I think, but I'm unsure if it's an independently-evolved English phrase or an import from one of the other languages that share it.
Loyalty/faithfulness (to a person, a cause, or a belief) in the sense of being particularly devoted and reliable and trustworthy, which is viewed as positive because nobody wants a backstabbing friend/relative/partner/underling that can't counted on. It could be used for a person loyal to something you perceive as wrong (where you're not calling them stupid for not noticing they're in the wrong, but acknowledge a virtue they profess), and for the negative type of loyalty you'd use "blindly loyal" or "blind faith". I haven't myself encountered it being said directly to the person it's meant to describe (I'd expect it to be about somebody being talked about but not talked to, e.g. "oh, there's no way Max would cheat on Alex with that sexy/hunky co-worker he's with on a week-long business trip, he's as faithful as a dog").
Specific expressions like this one are idiomatic and take time to form (their spread relies on cultural exchange with neighboring lands, culture pushing in case of territories of former empires and big, old religions, and groups of migrating people used to their own idioms spreading them as calques), so they may not work as well when directly translated or taken out of their native habitat (but you can probably find the concepts behind them expressed differently in your language/culture - in this case it could be reliability based on another critter, a sturdy object, a historic/mythological/religious figure famous for it, or maybe a predictable natural phenomenon).
Sorry if you already know it and the explanation was unnecessary.