EP3 Si Acceleration problems. Big nightmare

So i got a Civic EP3 Si in a november, its stock k20a3, only aftermarket muffler installed by previous owner.
Car is not bad at all in winter/cold spring condition but a big nightmare now in worm/hot weather.

BIG lag in acceleration, car acts different everytime i press the gas pedal.
It almost don't go at WOT, have way more power with the pedal pressed 20% than 50-100%
I press the gas pedal and instead of REVS go up and car take off it just go nowhere for 2-5 seconds then it "kick" and accelerate fine.

I already had my car in 3 different places for diagnostics, even in stealership they spent 5 hours to find the problem.
No results.
Already spent about 3000$ for diagnostics and parts but none of them helped.

So all the fuel pumps, fuel pressure, injectors, vacuum leaks, exhaust leaks, timing was TRIPLE CHECKED. And its good.

HERE is my shift from 2nd to 3rd at low rpms and WOT:
https://www.youtube.com/watch?v=19kBDM_ID3Y

(NEW) Upstream sensor DENSO 234-9004
(NEW) Downstream sensor DENSO 234-4122
(NEW) Serpentine belt
(NEW) OEM ELD (Electronic Load Detector) 8255-S5A-003
(NEW) OEM RELAY ASSY., FUEL PUMP (5P) OEM 39794-S5A-003
(NEW) OEM RELAY ASSY., ENGINE CONTROL MODULE (4P) OEM 39794-S5A-901
(NEW) OEM RELAY ASSY., POWER (4P)
(NEW) OEM PCV VALVE 17130-PRB-A01
(USED) OEM MAP SENSOR 37830-PGK-A01
(USED) OEM ECU 37820-PNF-A11
(NEW) Most of fuses
(NEW) Cat Converter
(NEW) NGK Spark Plugs
(NEW) Upstream sensor again...
(NEW) Intake air temperature sensor
(NEW) Coolant fluid flush

I replaced 2 months ago a o2 sensor for DENSO 234-9004, it was stuck at low voltage, reading lean, causing my ECU throws P0171 and runs rich. Car was making about 250km per TANK.
The ECU was switching between OL-CL like crazy all the time, doesnt matter it was on idle or driving or high load.

I replaced o2 sensor again for some OEM style ebay sensor, it reads full range voltage, its not stuck, its very active, ECU not throwing P0171 anymore but im getting a P1164 few times per day. Mileage is better, about 400km per TANK.
Car stays in CL, go to OL instantly after pressing gas pedal harder so seems to be good.

My battery light was always ON, even after replacing ECU, never came off even for 1 sec.
I had a code P1298 Electric Load Detector Circuit High Voltage, replaced the ELD brand new from stealership.
Didn't help, battery light stays ON.

My next thing is a TPS, but im thining if my cruise control works perfect, thats mean TPS should be good too?

Man this does sound frustrating. I'm NOT a mechanic by trade so take this with a grain of salt. The battery light on seems to indicate a faulty alternator. The alternator is not charging the battery and the battery is basically running the car. If it can't provide enough spark the car would not run well. It's also possible that the alternator is not providing enough voltage, or intermittent voltage, to your car. If your battery is tired now maybe try installing a fresh battery and see if the car runs better. If it does than you've figured out the problem. Good luck and make sure you post your results.