Two possibilities occur to me: a too-large turbo or a too-loose wastegate.
when I press the accelerator there is no power until the rpm
tachometer reaches 2500
This almost sounds like the replacement turbo is too large.
when I press the accelerator there is no power until the rpm tachometer reaches 2500, then I need to release the accelerator and then press it again and only then the power is back
Look at the whole combination, I wonder if the wastegate is staying open until you release the pedal and then re-apply. Do you have a boost guage? If so, are you seeing a slowly building boost with a sharper increase at 2500?
Note: even without a boost guage, you should be able to hear the turbo spinning up. If I drive with my windows up, radio and vent fans off, I can hear the turbo spin up and blow off in sync with the boost guage.
EDIT: based on the comments, I have to think that either the wastegate or the blowoff valve is opening when it should not. If the turbo is spinning, the wastegate has to be at least partly closed (to enable the exhaust gases to spin up the turbo). If the blowoff valve is opening at an odd time, the turbo could be spinning but venting the boost in a non-useful way.