FWIW, I've never heard anyone use the term spoons to refer to their degree of willpower. Rather, I've always heard people use the term spoons to refer to their level of physical energy/stamina.
For example, someone might say that having to stand (rather than sit) on public transit wiped out their spoons for the day.
If I heard someone say that clearing out their email inbox wiped out their spoons for the day, I would be surprised. I would assume they were using the term at an additional level of remove from the original metaphor. That's fine, but nonstandard in my experience.
Many tasks take both physical and mental energy, like running errands. So I can see how some people might assume, from hearing spoons refer to such tasks, that it meant both kinds of energy. Or they could assume the opposite from me in terms of which one it refers to more. Or, the consensus on its definition could be different now than a decade ago when I formed my impression. Still, here's my data point.
On muscle knots - whatever they are - it isn't just a difference in the experience of those who have them, but also those massaging them. For me they've always been obvious. When giving a massage, there are relaxed muscles, tense muscles, and knots, and these are three very different feelings regardless of whatever I'm massaging with fingers, palms, knuckles, elbows, or otherwise. It's very clear that a knot-feeling-recipient and I almost always agree on the locations of knots, or their absence (the exception seems to be knots that are "deeper" under an also-otherwise-tense area, in which case massage to remove the tension can make it possible for me to feel the knots). That, to me, is very strong evidence that something real that is being detected.
I only recently learned that this isn't the case for everyone, and that a non-knot-feeling person may have no idea what the other party means when giving a massage to a knot-feeling person. FWIW I experience this as a kind of nodule (some larger or harder than others) that sort of...clicks?... as my hands move over it, typically causing my movements to be less smooth as I move over that spot.
I think a better framing is "does this model pay rent in anticipated experiences?" (using the local lingo), not "legitimate or illusory".
A lot of people use "spoons" to refer to their degree of willpower. This is a kind of Ego Depletion effect, but the science on ego depletion seems to be somewhat contested at the moment. I think it's possible that rather than it being universal, there are some people for whom it is an effective explanation of their experience, while the majority of people don't experience it. This could be much the same as myofascial trigger points, or "muscle knots": for some people, their existence is obviously self-explanatory, as it's a component of their lived experience, where for others it seems like some manner of mystical mumbo-jumbo akin to acupuncture, and likely nothing more than a placebo-ish invention to sell more Massage Therapists. That they are difficult to reliably induce in a laboratory setting means that they have been poorly studied; we don't have a consistent method for inducing muscle knots across a population. And if we did, you'd be deliberately inducing pain on them - good luck getting that to pass ethics approval. As a consequence, many people don't think they have any basis in reality.
This all strikes me as the same sort of thing as mental imagery and aphantasia. Some people may colloquially referring to typical muscle fatigue as a "knot" in (what seems to them) a clearly allegorical sense, while others explicitly are using it to refer to a distinct phenomenon of tangible nodules of tight muscle fibres, which are (to them) clearly an actual thing. So I think Ego Depletion is legitimate, in the same way as Myofascial Trigger Points and Mental Imagery are legitimate, in the sense that there is a certain population who claim to experience it, and I don't see any particular reason to doubt those reports. Looking into it, I can't find any studies self-selected according to people who already believe that they suffer ego depletion, relative to those who don't - I would be very interested in the results of such a study. The closest I can find is this one, where the authors claim that belief in ego depletion causes ego depletion - but it seems more possible to me that directly experiencing ego depletion is the thing which is inducing the belief! I wonder how large the cross-populations are; those who experience it but don't believe it's legitimate, and those who don't experience it, but do believe it's legitimate. I imagine those groups are probably small relative to the experience-belief matching groups.
It's hard - perhaps impossible - to experimentally determine which elements of other people's lived experience are legitimate or illusory. Perhaps the question doesn't really mean anything?