One photon at higher frequency contains more energy?

Light (EM) intensity is a measure of the number of photons per unit time in the group wave.  So no matter what the energy E = hf, when you have N > n photons per unit time, the total wave energy TE = Nhf > nhF = te where f < F is possilbe when N/n > F/f so that N > n(F/f) must be true.  That is the number of lower energy photons per unit time N must be greater than the frequency ratio times the number of higher energy photons.  QED.

Turns out that higher amplitude waves can and do carry more photons per unit time than comparable lower amplitude waves.  This is why we find that EM intensity is proportional to the square of the amplitudes.

A heavy car at 50 mph has more energy than a light car at 50mph.

(For big energies) You can contain any amount of energy in a highway with many cars of any particular weight travelling on it at 50 mph. The amount of energy is related to the number of cars not the mass.

(Although is obviously is related to the mass too, but since all cars weigh similar amounts anyway the number of cars is more important)

You seem to then be mixing it up with information. We use laser's to carry info rather than x-rays for practical reasons, not because of information density.

In the classical description of a wave, the energy is proportional to amplitude squared. It is the size of the vibration, not the frequency, that contains the energy.

Actually, I think those are my words from an older answer. So perhaps I'm not the one to explain it better"The more it is vibrating the more energy it is carry"
In terms of amplitude, yes. Not in terms of the frequency of those vibrations."Laser have wavelength that vibrates slower than x-rays ."
Yes. Laser frequencies are slower than x-ray frequencies."And is limited on how much it can carry."
A pure frequency carries no information. You add information by modulating the amplitude and frequency, which causes your wave to contain multiple frequencies.

If you put 2 MHz of information on a laser or an X-ray, they both are carrying about 2 million bits per second of information. It is not the base frequency of the laser or X-ray that matters.

"But x-rays vibrate more than laser so can carry more information"
It is not the base frequency of the vibration that matters.