It is true, and as i said, there was good reason for Emperor not to show his power in front of people. But there is smth i cant understand about it.Those are things that it's actually precedented for the Emperor to do when the Imperium as a whole is threatened in 40k. But having the Emperor walk around having psionic armwrestling matches and blowing up giant robots with his brain is not so probable.
As Simon noted "It might actually be easier to start with "what are truly, deeply, impressively high-end psykers and sorcerors capable of in 40k?" Because that at least establishes a baseline for what the God-Emperor is more capable than." And we know what they can do- from lightnings, fireballs, TK and stuff to tering the fabrics of reality and brainwashing entire populations of Hive worlds and even sectors. Actually we see these "psionic armwrestling" and killing tanks and stuff in 40k- and given available info about Emperor- he is capable of feats immensely greater(he can without any problem sit on a throne that killed second most powerful psyker in no time and as far as i know he keeps chaos gods in warp) - so why didnt he start to use these powers when Horus heresy obviously began and all his worries about ppl worshipping him actually didnt matter at all?
And about the Storm of the Emperor's Wrath- its really unknown whether it is really Emperor s intervention or no- it is said that Thor just believes storm to be it- thats all.