> They don't seem to have much bearing on the question of whether we're improperly classifying two separate phenomena as the same thing.

Ok, let's address this directly.

First I should note that your account is entirely anecdotal,
so I have no real tools to argue you out of this position, as you weren't argued into it in the first place.
You saw these things and developed a theory that you believe explains your experiences.

First, I think we should take a step back and first discuss what it means to be visibly trans.
For the purpose of this discussion, I'd give this simple definition:
Having gender dysphoria (or euphoria) and changing one's presentation in society to align with their preferred gender.
This can also include medical interventions ranging from HRT to surgeries, and legal remedies like changing one's passport and birth certificate.

I'm assuming you probably this definition unobjectionable.
However, from here, you assert you'd like to make another division.
'trans fake/delusional' and 'trans real'.
And I'd like to ask you what the purpose of such a distinction would be.
Your stated diagnostic criteria for fakeness are as follows:
A: "personality shifts radically" (not exclusive to trans people: gay people coming out, going to college, dating someone new, having kids, got sober, started smoking weed a lot)
B: "exaggerated caricature of their target gender" (not exclusive to trans people: gigachad meme, cis female models, whatever goop is, male weightlifters, bro culture broadly)
C: "difficult time with same-gender small group dynamics". (not exclusive to trans people: I've met lots of cis boys and girls struggling with this, fewer adults, but still common enough)
D: "spiraling?" (not exclusive to trans people: tons of mental illnesses, difficult circumstances, trauma)

Let's now interrogate the usefulness of this distinction in three contexts
Medicine:
Let's imagine for a second you are a doctor and you have two patients that are asking for testosterone.
Both describe feelings of gender dysphoria, both have begun to transition socially.
One is buff and crass with a manly hair cut, casual clothes, and an easygoing nature, you chat about football and whiskey.
The other is demure, awkward, and shy. As if compensating, he is wearing what you consider to be a caricature of manly fashion, and he speaks with a silly sounding (to you) deep voice.
It's clear he's uncomfortable being in the room with another man.
Does your course of treatment change?
If not, then the distinction is meaningless in the medical context.
If so, see my previous comment.

Legal:
You are now a county clerk, you are faced with the same two patients above 2 years later.
Both are seeking to change their legal name.
The demure one now has a full beard and has filled out a bit, but you can still see the 'fakeness'.
He talks about going out shooting, but it's clear he has yet to grasp the fine details of the 'male' culture he's trying to emulate.
Do you deny him his name change?
If not, then the distinction is meaningless in the legal context.
If so, ... that's illegal, don't do that.

Social:
You are at a party now, same demure guy as before.
He's trying to flirt awkwardly with another man, you can tell he's overcompensating and tripping over words.
Do you treat him differently than your 'real trans' friends?
If not, then the distinction is meaningless in a social context.
Do you treat him differently than your other 'awkward' friends?
If not, then perhaps this is the right label.

So having explored some of the ways the distinction might be employed, what then is left?
What is more 'proper' about this new distinction that warrants its creation?

Having pondered this for some time, I believe that your first comment boils down to:
Some trans men and women can be awkward, cringe, flamboyant, fragile, or performative in a way that makes you uncomfortable and/or suspicious.
In response, you think their transness is inauthentic and you'd like to put them in a different trans specific social box (that you invented).

Boxing stuff in and of itself is standard human behaviour, but it's important not to make this kind of thinking 'official'.
If it were made official, it would make each of the categories above needlessly more difficult for trans people.
Moreover, for older LGBTQ+ people reading this, the arguments about 'real' and 'fake' sound disturbingly similar to time-worn arguments used to invalidate them.
"Bi people are just straight and faking it to be different."
"Bi people are really just gay and don't want to admit it."
"Ace people don't really feel that way, they just haven't met me yet snickers"
"Demi people aren't ace at all, they are just faking."

The list goes on, the arguments become tedious, and for me, it mostly boils down to this:
Why should anyone care if random acquaintances met in passing are 'fake' or 'real' {insert minority status or mental illness here}
I'd much rather accidentally accept a 'faker' than reject someone from misplaced suspicion.
Honestly, I don't perform this kind of calculus at all in my day to day life.
To my knowledge, I've never met a malingerer of any kind, and I don't think I'd be anything other than mildly irritated if I did.

If you find the 'fake' trans people you meet to be annoying, use the label 'annoying' instead and don't hang out with them.
It's far easier than inventing a new category of trans person, when the existing social labels like 'weird', 'over the top', or 'a total mess' are already sufficient.