You're spot on, I'm sorry for my loose usage of the term.
But I dont necessarily fully agree with your definitions either. Don't get me wrong they are soundly constructed, I just don't personally see it the same way. The slur one is fine and I largely agree.
As for the ideological definition I'm not sure that you can decidedly say that self-improvement is at odds with it.
I think a full definition for me would be mostly related to the culture of specific online spaces, what I would call "4chan social dynamics" and it's memes and people who buy into them past a certain point, and very little to do with any sexual status or lack thereof, which there's nothing actually wrong with, it's fairly obvious that lack of sexual access for men is a significant detriment to their quality of life and it's complex societal problem to be solved like any other. It's not for me to really talk about at length because I'm not a man.
I would argue though that "femcels" in communities like FDS and (I'm not sure if it's a thing still) Vindicta are very much thinking along the exact same lines despite very few of them being involuntarily celibate or identifying with the label in any significant way.
Likewise men who have sex but still buy into these memes are also still ideologically incels under this definition.
I think this grouping is more useful because it allows us to identify ideological and philosophical commonalities between more stereotypical incels and those who wouldn't on the surface be such.
What I've found across my observations is if grouped this way, plenty of these people actually do practice self-improvement and are explicitly motivated to do so via their ideology. A particular telltale sign is active hostility and contempt towards those who do not buy into the same memes.
So I don't necessarily see a toxic variety of "self-improvement" as being contrary at all to this ideology, in fact if anything I see the "blackpilled" (or in less internet terms - hopeless) variety as being far less harmful than the "redpilled" variety which is often used to exploit people economically via endless lifestyle coaching guides and courses and even transparent pyramid schemes alongside usually a serving of mysogyny and reducing women's behaviour to some sort of conspiratorial pseudo-scientific evolutionary psychology "harsh truth" that only serves to further disconnect people from the real world and entrap them in cycles of financial exploitation.
In plain English, in the best case the very framing of "work out to get a girlfriend" is inherently distorting reality into 4chan social dynamics and implying a causality that isn't there (e.g. "guys who work out get girls") when in reality women aren't something to "get", and many men don't work out and have women all the same.
Through this lens "looksmaxxing" is problematic the same way those fake "diet" aids are, even when the implication is unspoken.
When you introduce the profit motive into this, there's never any incentive for people to get out of the cycle, only deeper in.
In contrast the ones who think self-improvement is a cope maybe have some unproductive ideas but honestly I just don't think people holding communions of shared self-loathing is a particularly huge problem unless they threaten and go through on real world harm ala Elliot Rodgers or whatever his name was.
Also sorry for the long-winded response, I just want to add that I may sound overly harsh on self-improvement but this is coming from someone who is a staunch self-improver myself.
I'm not at all against self-improvement in the slightest, but I think it's important to work towards whatever goals one may set for the right reasons as well, and recognize when a drive for self-improvement stems from a "toxic" (less productive) place and when it stems from a "legitimate" place (actually solves problems).
