ABS Pump issue (pump motor replaced)

Sorry for the quite long story here, but I'm feeling like I'm still in the middle of it.

2005 Prius with the ABS, VSC, brake light problem. All light up, the assisted brake was gone, plus the continuous beeping alarm noise.

Used a tester and identified the C1256 code - Accumulator Low Pressure. Also didn't hear the little pump engine working at all. Decided to take out the ABS assembly and see what could be the problem.

Identified that the ABS pump motor was gone, took it out of the assembly to see if it works, but it didn't turn at all, when hooked up to 12v, opened it up and found why it was seized up: full of rust and with two of the magnets detached from the case and stuck to the rotor. Also the rotor looked and smelled burned - didn't measure it but was garbage anyway.

Figured out that most probably the motor was causing the low pressure. From all available options for me, decided to buy a new motor (from China) and replace it in the assembly (a new pump was out of the question expensive, and used ones I really didn't trust by the looks of those available in my area, also read about others going through 3 used ones and still no fix).

I've put the whole ABS assembly back to the car, connected all lines very carefully - no leaks.

Did all that work myself, and only asked a mechanic-enthusiast neighbor for help with a compatible tester - that looked to be capable of air bleeding for Toyota. Turned out it was only sort of guiding us through manual air bleeding and didn't actually electronically air bleed the pump - or maybe we didn't explore all the available options of that software. Managed to air bleed the lines for each wheel (I hope), but I don't think we've got the air out of the pump itself, as it never got to that stage of pressing the pedal 30 times in 30 seconds that I saw other testers or Techstream required.

Now I still have codes for low pressure. But while doing the air bleeding the manual way, I saw that the pump motor used to crank and build pressure every time we took out the R8 (ABS MTR) Relay, the pump motor starts pumping and the errors and beeping goes away. Then if I press the pedal a few more times it cranks again and rebuilds it, but after a few presses the codes and beeping comes back. And if I repeat the relay take out process it builds pressure back again, and so on.
Also I noticed that the regular bussing of that little pump motor that we hear every time we open the driver door after it's been sitting for a while doesn't happen. I only hear the relay clicking, an no motor buzzing. An when I press the pedal I think I hear the solenoids working.

A few days ago I managed to get a Mini VCI and installed Techstream and get them properly working. Cleared codes and rebuilt pressure like I've described above (taking out the relay), the C1252 still lingers. As I'm preparing to do a complete ABS Pump air bleed, my question is: do I need to measure or replace relays to prepare for the air bleed?