Aloy collecting that part of the Sylens' weapon had no impact. It was a catalyst for testing the weapon and was rendered useless after the weapon self-destructed (Telemetry Log) and purged all data within the core (as mentioned by GAIA after scanning it in Cradle of Echoes).

But still that weapon part was used to make exact copy of that weapon so maybe without that party it would be impossible. Noone knows.

Where is this stated?

Aloy got that part after it had been used to disable Verbena's shield, noting that the Oseram wielding it was sending data on the weapon elsewhere, with the datapoint Telemetry Log obtained at the same time confirming this, and GAIA noting that the core had purged the data once the malfunction took place to stop anyone else from using the weapon. After this, the part is kept in the same room where overrides can be repaired, so Sylens didn't use it beyond the test to make the final weapon.

Why not. Maybe this part is exact same as the one in the final weapon especially that when Aloy went to Sylens after he made and upgraded that weapon he was in her base not somewhere else right? So possibly he used the part that Aloy took. Otherwise taking it by Aloy would be pointless. If im not wrong all that Aloy did was bringing this weapon piece to Gaia and then she scanned it and thats all. They needed Sylens to upgrade it and make it work.

Unless that "ball" is somewhere in the room even after Sylens made that weapon so ok...

I think that's incredibly doubtful since the part remains in the Base in the exact same place, with Sylens' weapon (fully intact) appearing in the common room after completing Singularity.

Also when Aloy was talking about that part with Gaia she was said something like "what if we could recreate and upgrade it maybe Zeniths wouldnt be so invincible after all" or something like that. So thats why i thought this exact part was used in weapon.

True. But unfortunately, it did prove useless.

Yes, there weren't many Zeniths left.

Are there any left?

@Lethal blade00 As far as we know, there are no Zeniths left. All thirteen who returned to Earth have been killed, and many were killed by Nemesis on Sirius. We don't have solid confirmation that all of the remaining ones on Sirius were killed, although I think it's reasonable to assume none have survived.