> I'm very sure that you are wrong here

What actual textbooks on relativity have you studied? If you haven't studied any, I would strongly suggest doing so before being this confident about your beliefs about relativity. Many pop science sources (including, unfortunately, books by physicists who should know better but who can't help themselves when there are no other experts peer reviewing their work) will say the kinds of things you're saying about photons "not experiencing time", but you won't find a textbook or peer-reviewed paper that says them, because such misstatements are weeded out. Sean Carroll has a set of free online lecture notes [1] that make a good start (they're more focused on GR than SR but they have an introductory section that covers SR). Taylor & Wheeler's Spacetime Physics [2] is a good introductory textbook as well.

The fundamental physical point here is that timelike objects (objects with positive rest mass that follow timelike worldlines) and lightlike objects (objects with zero rest mass that follow null worldlines) are different things, and the concept of "experienced time" or "proper time" (the latter is the correct technical term) only applies to timelike objects. The mathematical basis for this is that timelike worldlines can be parameterized by arc length, and arc length along a timelike worldline corresponds to elapsed time on a clock following that worldline. Null worldlines, however, cannot be parameterized by arc length at all, so the fact that arc length along them is zero does not mean lightlike objects "experience no time", it means that the whole concept of "experienced time" doesn't even work for them: it's mathematically invalid since it requires parameterizing the worldline by arc length.

Another way of seeing the fundamental difference is to look at how Lorentz transformations act on timelike and null vectors. Lorentz transformations hyperbolically rotate timelike vectors: that means the transformation changes which way in spacetime the vector points, without changing its length. But Lorentz transformations do not rotate null vectors: they dilate them, meaning they increase or decrease all components of the vector by the same factor, without changing its direction in spacetime.

This means that a null vector is not a "limiting case" of any set of timelike vectors as far as the Lorentz transformations are concerned; null and timelike vectors are simply two disconnected sets of vectors with respect to Lorentz transformations. Which in turn means that the common pop science image of objects "experiencing less time" as they move faster and faster, until photons moving at the speed of light "experience no time" in the limit, is not correct: it is not a valid description of what is actually happening in the math. Lorentz transformations don't change the length of timelike vectors at all, so they don't change the "experienced time" along them. The apparent "time dilation" of an object that is moving relative to you is due to the angle in spacetime between your worldline and the object's worldline, not to any property of the object's worldline itself. But the "angle" here is a hyperbolic angle, and the hyperbolic angle between your worldline (you being a timelike object) and any null worldline (i.e., any worldline of a light ray or photon) is infinite--in other words, mathematically ill-defined.

In short, pop science authors who make claims like "photons don't experience time" are putting an interpretation on the fact that a photon's worldline has zero length in the Minkowski metric that is not justified by anything in the actual math. They do it, unfortunately, because they believe (quite possibly correctly) that saying things like that, even if they're wrong, will sell more books than trying to teach their readers the actual science.

[1] https://arxiv.org/abs/gr-qc/9712019

[2] https://www.eftaylor.com/spacetimephysics/