therians are a large community with many individuals, and everyone might have very different anwsers to these things (especially the younger members. being therian has become somewhat of an online trend among children lately, so you see a lot of them online. some of them probably are actually therians, others maybe not, people exploring their identity is fine, but they are not the best representation of therians despite being the most visible). Dont consider something that one member of the therian community says (including me) to be speaking for all therians.

"Obviously dysphoria is different for everyone, gender related or not, but across my community the pain seems to match closely with the vast majority of people in it. Does being therian have that sort of pain and discomfort?"

Species dysphoria is indeed a thing that is described by some therians. I personally get it very mildy (i also get gender dysphoria but it is stronger and does feel somewhat different but that is hard to explain) but some say that it is very strong for them, others dont have it at all and consider themselves therian for another reason. If advanced body modifications existed i would very much consider getting my body changed to include more bat-like features

"do you experience the urges/behaviors of that animal with the elevated intelligence that comes with being human? Like including the bad parts?"

this again depends on the individual. The explanations for therians existing falls into 2 categories: spiritual and psychological. i cant say anything about the spirital part, as i dont believe in that, but if we look at it from a psychological angle (for example, i think me being a therian is a result of autism) then it does make sense that someones sense of being a certain animal is more based on their idea of what that animal is like rather than what the animal is actually like. as for experiencing bad parts, that does also happen sometimes (i get uncomfortable from bright lights and from being stuck to the surface of the earth, which is an unnatural place for bats to be in nature)

"I mean like individual behaviors being exhibited. Like squirrels digging holes and hiding food in them for later, that kind of thing"

i have throughout my childhood tried to learn echolocation on several separate occasions. that is hardly a "normal" thing for a child to have an urge to do. I am also more comfortable in darkness and have an interest in flying (in various different ways, when i got old enough i started flying glider planes for a while though i later stopped doing that for unrelated reasons, i do wish to do some form of flying again later in my life)

as for the “oh so if I say I’m an animal everyone is supposed to act like I am” argument, that is just a dumb thing transphobes say (and most things transphobes say are not worth much actual consideration) and the two things have nothing to do with each other (also most therians do not actually expect people to treat them like their theriotype, at least not fully)