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So why does it happen that the speed does not change in non-uniform magnetic fields?

I read this post Speed of a charge in a magnetic field but the answer seems a little inconvenient.

My question is that if the magnetic field is changing then it should apply an induced electric field, right? For example - if it is a time-varying circular magnetic field, then the induced electric field will form circular loops. Then why doesn't the velocity change for charged particles moving in that field at an angle (between the velocity and the induced field) which is not 90 degrees, because the work done is zero.

Maybe I don't know about some important concept of a non conservative field.

Thank you for your time!

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A fundamental reason that a static magnetic field cannot change the speed of a charge is that the force exerted by the field is always perpendicular to the velocity of the charge.

Your question seems to be different from what the title indicates: it seems that actually you are want to know if the electric field induced by a time-varying magnetic field can increase the speed of a charge. The answer is "yes", for the reasons you describe.

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You text is not very readable. In the rest frame of the magnet the magnetic field is not changing and there is no electric field. In other words no work is done on the particle.

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