quantum field theory - What is the meaning of the size of a particle in QFT?

I have often seen people refer to the size of a particle being at most a given value, or a particle being a point particle, in the context of quantum field theory. Examples are the Wikipedia entry on the electron, where it says

Observation of a single electron in a Penning trap shows the upper limit of the particle's radius is $10^{-22}$ meters. Also an upper bound of electron radius of $10^{-18}$ meters can be derived using the uncertainty relation in energy.

or the accepted answer to the related question Do electrons have shape?, which starts

As far as we know the electron is a point particle

this answer to a physics stackexchange question which mentions

an upper bound on the [electron] radius of $10^{-22} m$

or in the particle adventure by the particle data group

We don't know exactly how small quarks and electrons are; they are definitely smaller than $10^{-18}$ meters, and they might literally be points, but we do not know.

However, in QFT a particle is a quantum of excitation of a field (see e.g. the concept of a particle in QFT, which doesn't explicitly talk about size or point particles), and it is not so clear what would be the meaning of the concept of size.

I have also heard "probing a system at a length scale" in these contexts, like in the aforementioned answer this answer in which it says

What they actually list in that reference is not exactly a bound on the electron's size in any sense, but rather the bounds on the energy scales at which it might be possible to detect any substructure that may exist within the electron. Currently, the minimum is on the order of 10 TeV, which means that for any process occurring up to roughly that energy scale [...], an electron is effectively a point. This corresponds to a length scale on the order of $10^{-20}$ m, so it's not as strong a bound as the Dehmelt result.

From that I infer that he means that a point particle is a particle with no substructure (whatever that exactly means). A possibly non-point particle may look pointlike up to a given energy scale, which seems plausible enough. To translate this into a length scale, you convert to the correct dimensions using factors of $c$ and $\hbar$.

Is it really an energy scale we are talking about when referring to the size and is it just a manner of speech to call this an upper bound on the size of the particle? Does it have any meaning as an actual size?

Finally this answer to a somewhat related question states that

Pointlike is a technical term that refers to the fact that in the standard model, the Lagrangian is a function of fields at the same point (rather than of integrals over fields in some small neighborhood of this point ...)

which seems to suggest that the size of a particle might be defined as the distance up to which the values of the field influence the value of the Lagrangian density at a point. Is that a sensible interpretation of the size? Is it equivalent to the other possible meaning (as the length corresponding to the energy below which no substructure can be detected)?