Ok, let me give it a try. I am trying to not spend too much time on this, so I prefer to start with a rough draft and see whether there is anything interesting here before I write a massive essay.
You say the following:
Do chakras exist?
In some sense I might be missing the point since the answer to this is basically just "no". Though obviously I still think they form a meaningful category of something, but in my model they form a meaningful category of "mental experiences" and "mental procedures", and definitely not a meaningful category of real atom-like things in the external world.
Another way might be that you think chakras do not literally exist like planes do, but you can make a predictive profit by pretending that they do exist
I don't think the epistemically healthy thing is to pretend that they exist as some external force. Here is an analogy that I think kind of explains the ideas of "auras", which is a broader set than just chakras:
Imagine you are talking to a chessmaster who has played 20000 hours of chess. You show him a position and he responds with "Oh, black is really open on the right". You ask "what do you mean by 'open on the right'?". He says: "Black's defense on the right is really weak, I could push through that immediately if I wanted to", while making the motion of picking up a piece with his right hand and pushing it through the right side of black's board.
As you poke him more, his sense of "openness" will probably correspond to lots of proprioceptive experiences like "weak", "fragile", "strong", "forceful", "smashing", "soft", etc.
Now, I think it would be accurate to describe (in buddhist/spiritual terms) the experience of the chessmaster as reading an "aura" off the chessboard. It's useful to describe it as such because a lot of its mental representation is cached out in the same attributes that people and physical objects in general have, even though its referent is the state of some chess-game, which obviously doesn't have those attributes straightforwardly.
My read of what the deal with "chakras" is, is that it's basically trying to talk about the proprioceptive subsets of many mental representations. So in thinking about something like a chessboard, you can better understand your own mental models of it, by getting a sense of what the natural clusters of proprioceptive experiences are that tend to correlate with certain attributes of models (like how feeling vulnerable around your stomach corresponds to a concept of openness in a chess position).
You can also apply them to other people, and try to understand what other people are experiencing by trying to read their body-language, which gives you evidence about the proprioceptive experiences that their current thoughts are causing (which tend to feed back into body-language), which allows you to make better inferences about their mental state.
I haven't actually looked much into whether the usual set of chakras tend to be particularly good categories for the relationship between proprioceptive experiences and model attributes, so I can't speak much about that. But it seems clear that there are likely some natural categories here, and referring to them as "chakras" seems fine to me.