I think it's a valid question, and personally I'm not offended by any of your phrasing. I will preface this by saying that although I am trans, I am not a furry. I do know a lot of furries. While I can't speak for them, I can relate things that I have picked up in conversation or observation.

So, because I know them through a mostly queer friend group, almost all the furries I know are also trans, which sort of complicates any answer they or I could give you. I will say that there is definitely an intersection between trans and furry, which isn't too surprising I think. As you noted, most furries don't literally want to transform into anthropomorphic animal characters. But those characters can serve as an outlet for feelings of dysphoria, or other forms of body image issues. One trans furry I know had a feminine fursona long before she ever realized she was trans. I think it's safe to say that the fursona was a way for her to explore feelings that she hadn't quite grappled with. She knew identifying with this character made her happy, but didn't fully grasp why until recently. For any trans furry, the fursona is a body they have complete creative control over, and that can doubtless be empowering. I get a (probably) similar feeling from creating a video game character that looks how I want to look. Crafting an idealized body tickles something deep inside.

But these could be edge cases. After all, not all furries are trans. How similar a cis furry experience is to the trans experience isn't a question I can really answer, but I suspect that there is no single answer. And the level that any given furry fully identifies with their fursona is highly variable. For some, it's just a fun character to put on, but for others it's more than that.

I hope I've been of some help, since I can really only approach this from one angle. It's a complicated question that I don't think there is a definite answer for, given the breadth of both trans and furry experiences.

I think a first step is to not get too hung up on labels and instead focus more on needs and actions. I will say that one should respect the label a person selects for themselves (i.e. how they identify), but often when a person is questioning I'll advise them to focus less on who they are or how they identify and instead focus on what they want to do. That often clears things up for them a lot and then typically after they better understand their own needs they then figure out the correct label for themselves.

As a concrete example, a person who neither identifies as male nor female (i.e. non-binary) might still want to undergo feminizing or masculinizing HRT, which is one way you get people who identify as "nonbinary trans".

hi, cis furry within that small demographic here. my experience is like. yes, optimally, i would be a funny animal irl. but i don't consider myself trans because that funny animal is still male. i have some friends who are trans and furry who also would like not to be human (one of them even made an NSFW game about it, so there definitely is Something, but i'd agree that it doesn't need to be labeled. i kinda like that the furry/therian/trans connection is one that is unexplained/unlabeled y'know. leaves a lot of room.

a big part of it for me is motion--movement is part of presentation, and i get an absurd amount of gender envy from the energetic squash-and-stretch femininity of the Thomson cat. when i watch video of myself moving, i often feel like i'm moving too squarely, and my fursona lets me show the absurd extent to which i want my movements to exist that often isn't possible within the human form. you'll def get a different answer from everyone but that's mine, thanks. hope it helps make this weird unfocusable thing a lil more grokable.