Brake Booster Pump Motor running too often and too long after replacement

I have had issues with the brake booster in my Gen 3 Prius and the details of that can be read in this post ABS, Brake and Traction lights on with codes C1252, C1253, C1256, C1365 | PriusChat

The long story short, I had codes C1252, C1253 and C1256 hence replaced the brake booster pump motor only with a used/reconditioned unit around a month ago.

I have never replaced the brake fluid in my 4+ years of ownership of the vehicle and I am not sure whether the previous owner replaced it either. I only topped up the brake fluid reservoir with Toyota DOT 3 as much as required during the pump motor replacement procedure.

Recently, I noticed that the pump motor runs for a significantly longer duration than usual when the car is unlocked and the driver-side door is opened. I have also noticed that the pump motor sometimes runs every 10 seconds or so even without the brake pedal pressed.

However, I have got the ABS and brake lights on again with beeps, scanned only to find the same following codes -

C1252 Brake Booster Pump Motor on Time Abnormally Long
C1253 Pump Motor Relay
C1256 Accumulator Low Pressure

The workshop where I had the pump motor replaced has said that there could be internal leakage in the master cylinder which is why it can't hold up the pressure resulting the pump motor running overtime. Although there is no code C1391 for abnormal leakage yet.

I have uploaded a video here of the specimen that shows brake pressure falling and the pump motor running without the brake pedal pressed for you, the experts here for a better understanding of the issue I am describing.

Do I now need to replace the master cylinder as well?